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12841 Reputation

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11 years, 67 days

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These are answers submitted by acer

One way this can happen is if you are in 2D Input mode, trying to make multiple statements in a single paragraph, and forget the trailing semicolon (or colon) at the end of a line (not the last one).

For example,

restart

n := 5;

5

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

Error, illegal use of an object as a name

"13  n:=n+1"

13; 1; n := n+1

13

6

 

Download illegal.mw

But that's just a guess. There are other ways to generate that error message. We cannot diagnose the particular problem unless you upload a worksheet that exhibits it.

Try the commands DocumentTools:-RemoveTask or DocumentTools:-RemovePaletteEntry .

You can use fdiff or evalf(D(...)) as a means to get numeric differentiation of the procedure returned by your pds:-value(T(x,y), x=0) call.

It is more efficient to call pds:-value(T(x,y), x=0) just once, before forming procedure Ty, than to have Ty form it for each input y0.

Here are some variants:


 

restart

plots:-setoptions(gridlines = false);

PDE := [(x*y+1)*(diff(f(x, y), y, y, y))+(x+((n+3)*(1/4))*f(x, y))*(diff(f(x, y), y, y))-((n+1)*(1/2))*(diff(f(x, y), y))^2+T(x, y) = (1/4)*(1-n)*x*(diff(f(x, y), y))*(diff(diff(f(x, y), y), x))-(1/4)*(1-n)*x*(diff(f(x, y), x))*(diff(f(x, y), y, y)), (x*y+1)*(diff(T(x, y), y, y))+(x+((n+3)*(1/4))*f(x, y))*(diff(T(x, y), y))-n*T(x, y)*(diff(f(x, y), y)) = (1/4)*(1-n)*x*(diff(f(x, y), y))*(diff(T(x, y), x))-(1/4)*(1-n)*x*(diff(f(x, y), x))*(diff(T(x, y), y))]

[(x*y+1)*(diff(diff(diff(f(x, y), y), y), y))+(x+(1/4)*(n+3)*f(x, y))*(diff(diff(f(x, y), y), y))-(1/2)*(n+1)*(diff(f(x, y), y))^2+T(x, y) = (1/4)*(1-n)*x*(diff(f(x, y), y))*(diff(diff(f(x, y), x), y))-(1/4)*(1-n)*x*(diff(f(x, y), x))*(diff(diff(f(x, y), y), y)), (x*y+1)*(diff(diff(T(x, y), y), y))+(x+(1/4)*(n+3)*f(x, y))*(diff(T(x, y), y))-n*T(x, y)*(diff(f(x, y), y)) = (1/4)*(1-n)*x*(diff(f(x, y), y))*(diff(T(x, y), x))-(1/4)*(1-n)*x*(diff(f(x, y), x))*(diff(T(x, y), y))]

 

sys_ode := diff(g(y), y, y, y)+((n+3)/4)*g(y)*(diff(g(y), y, y))-((n+1)/2)*(diff(g(y), y))^2+h(y) = 0, (1(1-λ)/10+1/1)*(diff(h(y), y, y))+((n+3)/4)*g(y)*(diff(h(y), y))-n*(diff(g(y),y))*h(y) = 0

diff(diff(diff(g(y), y), y), y)+(1/4)*(n+3)*g(y)*(diff(diff(g(y), y), y))-(1/2)*(n+1)*(diff(g(y), y))^2+h(y) = 0, (11/10)*(diff(diff(h(y), y), y))+(1/4)*(n+3)*g(y)*(diff(h(y), y))-n*(diff(g(y), y))*h(y) = 0

 

ics := g(0) = 0, h(0) = lambda, (D(g))(20) = 0, h(20) = 0, (D(g))(0) = 0

g(0) = 0, h(0) = lambda, (D(g))(20) = 0, h(20) = 0, (D(g))(0) = 0

Digits := 10

10

sol1 := dsolve([eval(sys_ode, n = 0), ics], numeric, output = operator, continuation = lambda)

[y = proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .9220907462515571, (1, 4) = 1.0, (1, 5) = -.38783340466369254, (2, 1) = .16735567649115993, (2, 2) = .4202740870445161, (2, 3) = .3373570222677326, (2, 4) = .7355419804808778, (2, 5) = -.37712948659838486, (3, 1) = .503981373982817, (3, 2) = .5163794040551701, (3, 3) = -0.19185064713216023e-1, (3, 4) = .49172724293359593, (3, 5) = -.3229448930949884, (4, 1) = .8416523710936388, (4, 2) = .4417990492201716, (4, 3) = -.16651332416146195, (4, 4) = .2977138055168734, (4, 5) = -.23454549848673548, (5, 1) = 1.1062594162789947, (5, 2) = .31549674554502644, (5, 3) = -.18074641710244985, (5, 4) = .1656168899679353, (5, 5) = -.14708087178570156, (6, 1) = 1.2861729052641508, (6, 2) = .20118216105468362, (6, 3) = -.14047902635042844, (6, 4) = 0.8647526508575375e-1, (6, 5) = -0.8263424709324725e-1, (7, 1) = 1.3974860750621676, (7, 2) = .11890906506576693, (7, 3) = -0.9294999327444896e-1, (7, 4) = 0.4326575279767381e-1, (7, 5) = -0.4313615270778873e-1, (8, 1) = 1.462026155282785, (8, 2) = 0.6667910031326235e-1, (8, 3) = -0.5593040786446294e-1, (8, 4) = 0.21068777926171442e-1, (8, 5) = -0.2150725154063105e-1, (9, 1) = 1.497740830391555, (9, 2) = 0.3603568604801351e-1, (9, 3) = -0.3167753384430381e-1, (9, 4) = 0.10096973148301623e-1, (9, 5) = -0.10438939815596704e-1, (10, 1) = 1.516864299292917, (10, 2) = 0.18960327498140035e-1, (10, 3) = -0.1722319045196687e-1, (10, 4) = 0.4793366106261327e-2, (10, 5) = -0.4988937027048127e-2, (11, 1) = 1.5268547661160343, (11, 2) = 0.9782165431635105e-2, (11, 3) = -0.910157017546314e-2, (11, 4) = 0.22637704730545526e-2, (11, 5) = -0.2364269412330906e-2, (12, 1) = 1.5319805288911161, (12, 2) = 0.49724019908313965e-2, (12, 3) = -0.47113528942048085e-2, (12, 4) = 0.10660248274790495e-2, (12, 5) = -0.11153042237558037e-2, (13, 1) = 1.5345743659775581, (13, 2) = 0.24984995067600896e-2, (13, 3) = -0.2401250250975525e-2, (13, 4) = 0.5011966820226343e-3, (13, 5) = -0.5248289826886877e-3, (14, 1) = 1.5358728194208906, (14, 2) = 0.12440119569314578e-2, (14, 3) = -0.12093215573985628e-2, (14, 4) = 0.23544738145817105e-3, (14, 5) = -0.2466587850586314e-3, (15, 1) = 1.5365173102346918, (15, 2) = 0.6148015308811455e-3, (15, 3) = -0.6032811800317005e-3, (15, 4) = 0.11055525378085771e-3, (15, 5) = -0.11584628661588081e-3, (16, 1) = 1.536834972545, (16, 2) = 0.30197726796083954e-3, (16, 3) = -0.2986490288978108e-3, (16, 4) = 0.51899799851421e-4, (16, 5) = -0.5439103696428884e-4, (17, 1) = 1.5369906451774888, (17, 2) = 0.14755307935715694e-3, (17, 3) = -0.14690575453443246e-3, (17, 4) = 0.2436052045018883e-4, (17, 5) = -0.25532771206319318e-4, (18, 1) = 1.537066559314411, (18, 2) = 0.7177236700295585e-4, (18, 3) = -0.7187729398053743e-4, (18, 4) = 0.11432662628093271e-4, (18, 5) = -0.11984713858579463e-4, (19, 1) = 1.537103419510933, (19, 2) = 0.3477022315080817e-4, (19, 3) = -0.35007749994105596e-4, (19, 4) = 0.5364472172783753e-5, (19, 5) = -0.5625174866621487e-5, (20, 1) = 1.53712124655263, (20, 2) = 0.167801854213613e-4, (20, 3) = -0.16983543378325293e-4, (20, 4) = 0.2516289536316785e-5, (20, 5) = -0.2640190816045617e-5, (21, 1) = 1.5371298351182954, (21, 2) = 0.8066191186382534e-5, (21, 3) = -0.821104246872564e-5, (21, 4) = 0.11795051188684695e-5, (21, 5) = -0.12391870423047207e-5, (22, 1) = 1.537133955359844, (22, 2) = 0.3859180935593867e-5, (22, 3) = -0.395755789320176e-5, (22, 4) = 0.5520931946642665e-6, (22, 5) = -0.5816313926576407e-6, (23, 1) = 1.5371359212718083, (23, 2) = 0.18341823395610769e-5, (23, 3) = -0.19019345748834397e-5, (23, 4) = 0.2576175590429348e-6, (23, 5) = -0.2730071797956253e-6, (24, 1) = 1.5371368515706798, (24, 2) = 0.8623290091477282e-6, (24, 3) = -0.9113341483838946e-6, (24, 4) = 0.1194038808143948e-6, (24, 5) = -0.1281526473802194e-6, (25, 1) = 1.537137285591093, (25, 2) = 0.39734387332399116e-6, (25, 3) = -0.4351065480638164e-6, (25, 4) = 0.5452376150027097e-7, (25, 5) = -0.6015514998812785e-7, (26, 1) = 1.5371374825833801, (26, 2) = 0.17577216090080783e-6, (26, 3) = -0.2066547856380797e-6, (26, 4) = 0.24065480347840778e-7, (26, 5) = -0.2823339143989368e-7, (27, 1) = 1.5371375668997003, (27, 2) = 0.7087967992164601e-7, (27, 3) = -0.9729618184580756e-7, (27, 4) = 0.9768720688503002e-8, (27, 5) = -0.13249689734274169e-7, (28, 1) = 1.5371375980011175, (28, 2) = 0.2201947952838702e-7, (28, 3) = -0.45280562029436684e-7, (28, 4) = 0.30887065486698873e-8, (28, 5) = -0.6248707867260407e-8, (29, 1) = 1.537137604689266, (29, 2) = .0, (29, 3) = -0.20841183539706994e-7, (29, 4) = .0, (29, 5) = -0.30115916942592686e-8}, datatype = float[8], order = C_order); YP := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .9220907462515571, (1, 3) = -1.0, (1, 4) = -.38783340466369254, (1, 5) = .0, (2, 1) = .4202740870445161, (2, 2) = .3373570222677326, (2, 3) = -.6895707858708219, (2, 4) = -.37712948659838486, (2, 5) = 0.4303279115075219e-1, (3, 1) = .5163794040551701, (3, 2) = -0.19185064713216023e-1, (3, 3) = -.3511517120118227, (3, 4) = -.3229448930949884, (3, 5) = .11097150746096335, (4, 1) = .4417990492201716, (4, 2) = -.16651332416146195, (4, 3) = -0.9501085499656597e-1, (4, 4) = -.23454549848673548, (4, 5) = .13459484654365939, (5, 1) = .31549674554502644, (5, 2) = -.18074641710244985, (5, 3) = 0.3411652766552317e-1, (5, 4) = -.14708087178570156, (5, 5) = .11093836320508359, (6, 1) = .20118216105468362, (6, 2) = -.14047902635042844, (6, 3) = 0.6927210396491991e-1, (6, 4) = -0.8263424709324725e-1, (6, 5) = 0.7246495203970743e-1, (7, 1) = .11890906506576693, (7, 2) = -0.9294999327444896e-1, (7, 3) = 0.6122617103835701e-1, (7, 4) = -0.4313615270778873e-1, (7, 5) = 0.4110148141424317e-1, (8, 1) = 0.6667910031326235e-1, (8, 2) = -0.5593040786446294e-1, (8, 3) = 0.42483062663230695e-1, (8, 4) = -0.2150725154063105e-1, (8, 5) = 0.21439202918624025e-1, (9, 1) = 0.3603568604801351e-1, (9, 2) = -0.3167753384430381e-1, (9, 3) = 0.26135864069716998e-1, (9, 4) = -0.10438939815596704e-1, (9, 5) = 0.10660108900785871e-1, (10, 1) = 0.18960327498140035e-1, (10, 2) = -0.1722319045196687e-1, (10, 3) = 0.14980312940540426e-1, (10, 4) = -0.4988937027048127e-2, (10, 5) = 0.5159686682556715e-2, (11, 1) = 0.9782165431635105e-2, (11, 2) = -0.910157017546314e-2, (11, 3) = 0.820665675837047e-2, (11, 4) = -0.2364269412330906e-2, (11, 5) = 0.24612927413180455e-2, (12, 1) = 0.49724019908313965e-2, (12, 2) = -0.47113528942048085e-2, (12, 3) = 0.4359613237292593e-2, (12, 4) = -0.11153042237558037e-2, (12, 5) = 0.11649711508526675e-2, (13, 1) = 0.24984995067600896e-2, (13, 2) = -0.2401250250975525e-2, (13, 3) = 0.22655973789531695e-2, (13, 4) = -0.5248289826886877e-3, (13, 5) = 0.549128934106459e-3, (14, 1) = 0.12440119569314578e-2, (14, 2) = -0.12093215573985628e-2, (14, 3) = 0.11583494838774682e-2, (14, 4) = -0.2466587850586314e-3, (14, 5) = 0.2582976297565444e-3, (15, 1) = 0.6148015308811455e-3, (15, 2) = -0.6032811800317005e-3, (15, 3) = 0.5848477187234688e-3, (15, 4) = -0.11584628661588081e-3, (15, 5) = 0.12136351684889346e-3, (16, 1) = 0.30197726796083954e-3, (16, 2) = -0.2986490288978108e-3, (16, 3) = 0.29237649937883e-3, (16, 4) = -0.5439103696428884e-4, (16, 5) = 0.56993214408891095e-4, (17, 1) = 0.14755307935715694e-3, (17, 2) = -0.14690575453443246e-3, (17, 3) = 0.14499494333704743e-3, (17, 4) = -0.25532771206319318e-4, (17, 5) = 0.2675702078834315e-4, (18, 1) = 0.7177236700295585e-4, (18, 2) = -0.7187729398053743e-4, (18, 3) = 0.7143005172186065e-4, (18, 4) = -0.11984713858579463e-4, (18, 5) = 0.1255997924657351e-4, (19, 1) = 0.3477022315080817e-4, (19, 2) = -0.35007749994105596e-4, (19, 3) = 0.3499403148041789e-4, (19, 4) = -0.5625174866621487e-5, (19, 5) = 0.589532422011194e-5, (20, 1) = 0.167801854213613e-4, (20, 2) = -0.16983543378325293e-4, (20, 3) = 0.17063175277423634e-4, (20, 4) = -0.2640190816045617e-5, (20, 5) = 0.27670182261114854e-5, (21, 1) = 0.8066191186382534e-5, (21, 2) = -0.821104246872564e-5, (21, 3) = 0.828660617992783e-5, (21, 4) = -0.12391870423047207e-5, (21, 5) = 0.12987213913763072e-5, (22, 1) = 0.3859180935593867e-5, (22, 2) = -0.395755789320176e-5, (22, 3) = 0.4010386715431575e-5, (22, 4) = -0.5816313926576407e-6, (22, 5) = 0.6095763839708823e-6, (23, 1) = 0.18341823395610769e-5, (23, 2) = -0.19019345748834397e-5, (23, 3) = 0.19350330892911135e-5, (23, 4) = -0.2730071797956253e-6, (23, 5) = 0.28612441556520465e-6, (24, 1) = 0.8623290091477282e-6, (24, 2) = -0.9113341483838946e-6, (24, 3) = 0.931230468673015e-6, (24, 4) = -0.1281526473802194e-6, (24, 5) = 0.1343101069871441e-6, (25, 1) = 0.39734387332399116e-6, (25, 2) = -0.4351065480638164e-6, (25, 3) = 0.44709019111609976e-6, (25, 4) = -0.6015514998812785e-7, (25, 5) = 0.6304549361391542e-7, (26, 1) = 0.17577216090080783e-6, (26, 2) = -0.2066547856380797e-6, (26, 3) = 0.21417714781972993e-6, (26, 4) = -0.2823339143989368e-7, (26, 5) = 0.29589957438210912e-7, (27, 1) = 0.7087967992164601e-7, (27, 2) = -0.9729618184580756e-7, (27, 3) = 0.10239949399678307e-6, (27, 4) = -0.13249689734274169e-7, (27, 5) = 0.13886315345671458e-7, (28, 1) = 0.2201947952838702e-7, (28, 2) = -0.45280562029436684e-7, (28, 3) = 0.4911313445931053e-7, (28, 4) = -0.6248707867260407e-8, (28, 5) = 0.6548948046607739e-8, (29, 1) = .0, (29, 2) = -0.20841183539706994e-7, (29, 3) = 0.24026825208835925e-7, (29, 4) = -0.30115916942592686e-8, (29, 5) = 0.31562937567380326e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.947670133699624e-8, (1, 4) = .0, (1, 5) = -0.16801628863722625e-8, (2, 1) = -0.5562688680729497e-9, (2, 2) = -0.21544394426163097e-8, (2, 3) = 0.287293894307546e-8, (2, 4) = -0.37357656722536194e-8, (2, 5) = 0.32217191547761024e-8, (3, 1) = -0.8350526558565278e-8, (3, 2) = 0.4134830634172977e-8, (3, 3) = 0.12491061704911204e-8, (3, 4) = 0.3909918765623829e-8, (3, 5) = -0.20757291059677243e-9, (4, 1) = 0.16671389719705844e-9, (4, 2) = 0.3648160715899586e-8, (4, 3) = -0.528396986802508e-8, (4, 4) = 0.4823828777432993e-9, (4, 5) = -0.2408743014606509e-8, (5, 1) = 0.5571634668634835e-8, (5, 2) = -0.5437715786747662e-8, (5, 3) = 0.33059473772110423e-8, (5, 4) = -0.32522595808460493e-8, (5, 5) = 0.24277913015859777e-8, (6, 1) = -0.25669375582958455e-9, (6, 2) = -0.24447686990555343e-8, (6, 3) = 0.37763491733330965e-8, (6, 4) = 0.16312740125029958e-9, (6, 5) = 0.2836817825937946e-9, (7, 1) = -0.32389377868904443e-8, (7, 2) = 0.1881042655673872e-8, (7, 3) = -0.11396650576233194e-8, (7, 4) = 0.10620111323548136e-8, (7, 5) = -0.9612930708926523e-9, (8, 1) = -0.18812922832728336e-8, (8, 2) = 0.14232046751044453e-8, (8, 3) = -0.1537803668361072e-8, (8, 4) = 0.1770842620028042e-9, (8, 5) = -0.15945787869057221e-9, (9, 1) = -0.4702411602328281e-9, (9, 2) = 0.320333402872091e-11, (9, 3) = -0.9185162120441862e-10, (9, 4) = -0.19095599932287843e-9, (9, 5) = 0.23643248136766287e-9, (10, 1) = -0.17417744006906416e-9, (10, 2) = -0.4092039771380655e-9, (10, 3) = 0.4774557415611376e-9, (10, 4) = -0.11595631798509842e-9, (10, 5) = 0.14655938678934742e-9, (11, 1) = -0.36430615951141193e-9, (11, 2) = -0.22503070324966588e-9, (11, 3) = 0.31318800713246974e-9, (11, 4) = -0.7102340842716831e-11, (11, 5) = 0.14634454169986603e-10, (12, 1) = -0.5396388972588783e-9, (12, 2) = -0.10024023632452876e-10, (12, 3) = 0.52585615313555275e-10, (12, 4) = 0.30763893139739825e-10, (12, 5) = -0.34005653195770876e-10, (13, 1) = -0.5943567114066009e-9, (13, 2) = 0.7448998028657788e-10, (13, 3) = -0.708034730465589e-10, (13, 4) = 0.26507725195353555e-10, (13, 5) = -0.3134708409282319e-10, (14, 1) = -0.5789647343263283e-9, (14, 2) = 0.6946997649814925e-10, (14, 3) = -0.8160855192822036e-10, (14, 4) = 0.12965812897819388e-10, (14, 5) = -0.16205118685268952e-10, (15, 1) = -0.5480288674538708e-9, (15, 2) = 0.3755086868784173e-10, (15, 3) = -0.50490114989597235e-10, (15, 4) = 0.32350773786510558e-11, (15, 5) = -0.4700861305885854e-11, (16, 1) = -0.5257284342112479e-9, (16, 2) = 0.10919861164588246e-10, (16, 3) = -0.19346772632557297e-10, (16, 4) = -0.11790344440137198e-11, (16, 5) = 0.832624535476741e-12, (17, 1) = -0.5155200016654919e-9, (17, 2) = -0.30465560714292855e-11, (17, 3) = -0.8267473293057957e-12, (17, 4) = -0.22320654114644123e-11, (17, 5) = 0.2400655612059856e-11, (18, 1) = -0.5133923272616294e-9, (18, 2) = -0.737945441660333e-11, (18, 3) = 0.64527937509837154e-11, (18, 4) = -0.18460323317176304e-11, (18, 5) = 0.21645324044442117e-11, (19, 1) = -0.5148896773711696e-9, (19, 2) = -0.6805942618791494e-11, (19, 3) = 0.7290389637347693e-11, (19, 4) = -0.1127780748270535e-11, (19, 5) = 0.1426574333434267e-11, (20, 1) = -0.5172260423041393e-9, (20, 2) = -0.4657799114489725e-11, (20, 3) = 0.5567830559435603e-11, (20, 4) = -0.5303365272165861e-12, (20, 5) = 0.7538287303084591e-12, (21, 1) = -0.5191746746088076e-9, (21, 2) = -0.25874975582162318e-11, (21, 3) = 0.3436128045689803e-11, (21, 4) = -0.15574116810816628e-12, (21, 5) = 0.30144441341623344e-12, (22, 1) = -0.5204375227141072e-9, (22, 2) = -0.11365161545683807e-11, (22, 3) = 0.1752985745214996e-11, (22, 4) = 0.3249627740759922e-13, (22, 5) = 0.5150782611193112e-13, (23, 1) = -0.5211213531601294e-9, (23, 2) = -0.3082774300480712e-12, (23, 3) = 0.6809547502858554e-12, (23, 4) = 0.10140915458196715e-12, (23, 5) = -0.6050324746005763e-13, (24, 1) = -0.5214281864248747e-9, (24, 2) = 0.7242912386800786e-13, (24, 3) = 0.10576899938353571e-12, (24, 4) = 0.1072206483365034e-12, (24, 5) = -0.9414790219756612e-13, (25, 1) = -0.5215366608792588e-9, (25, 2) = 0.1891469519098857e-12, (25, 3) = -0.14497650859163652e-12, (25, 4) = 0.8641875813257649e-13, (25, 5) = -0.9035857945464468e-13, (26, 1) = -0.5215615175319244e-9, (26, 2) = 0.17670718185401007e-12, (26, 3) = -0.2150167149653954e-12, (26, 4) = 0.5891552332814735e-13, (26, 5) = -0.7282784304094444e-13, (27, 1) = -0.5215650870134602e-9, (27, 2) = 0.11694313367520813e-12, (27, 3) = -0.20000655303758359e-12, (27, 4) = 0.3377761208360633e-13, (27, 5) = -0.53341189571616226e-13, (28, 1) = -0.521579349038632e-9, (28, 2) = 0.5209631819213893e-13, (28, 3) = -0.15467632068966293e-12, (28, 4) = 0.14064084565986249e-13, (28, 5) = -0.3672938482279342e-13, (29, 1) = -0.5216042456082603e-9, (29, 2) = .0, (29, 3) = -0.10651195375400426e-12, (29, 4) = .0, (29, 5) = -0.24309258949721638e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 29, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 29, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187987466566, (2) = 18446884187987467006, (3) = 18446884187987467270, (4) = 18446884187987467446, (5) = 18446884187987467622, (6) = 18446884187987467798}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc, g = proc (y) local res, data, solnproc, g, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .9220907462515571, (1, 4) = 1.0, (1, 5) = -.38783340466369254, (2, 1) = .16735567649115993, (2, 2) = .4202740870445161, (2, 3) = .3373570222677326, (2, 4) = .7355419804808778, (2, 5) = -.37712948659838486, (3, 1) = .503981373982817, (3, 2) = .5163794040551701, (3, 3) = -0.19185064713216023e-1, (3, 4) = .49172724293359593, (3, 5) = -.3229448930949884, (4, 1) = .8416523710936388, (4, 2) = .4417990492201716, (4, 3) = -.16651332416146195, (4, 4) = .2977138055168734, (4, 5) = -.23454549848673548, (5, 1) = 1.1062594162789947, (5, 2) = .31549674554502644, (5, 3) = -.18074641710244985, (5, 4) = .1656168899679353, (5, 5) = -.14708087178570156, (6, 1) = 1.2861729052641508, (6, 2) = .20118216105468362, (6, 3) = -.14047902635042844, (6, 4) = 0.8647526508575375e-1, (6, 5) = -0.8263424709324725e-1, (7, 1) = 1.3974860750621676, (7, 2) = .11890906506576693, (7, 3) = -0.9294999327444896e-1, (7, 4) = 0.4326575279767381e-1, (7, 5) = -0.4313615270778873e-1, (8, 1) = 1.462026155282785, (8, 2) = 0.6667910031326235e-1, (8, 3) = -0.5593040786446294e-1, (8, 4) = 0.21068777926171442e-1, (8, 5) = -0.2150725154063105e-1, (9, 1) = 1.497740830391555, (9, 2) = 0.3603568604801351e-1, (9, 3) = -0.3167753384430381e-1, (9, 4) = 0.10096973148301623e-1, (9, 5) = -0.10438939815596704e-1, (10, 1) = 1.516864299292917, (10, 2) = 0.18960327498140035e-1, (10, 3) = -0.1722319045196687e-1, (10, 4) = 0.4793366106261327e-2, (10, 5) = -0.4988937027048127e-2, (11, 1) = 1.5268547661160343, (11, 2) = 0.9782165431635105e-2, (11, 3) = -0.910157017546314e-2, (11, 4) = 0.22637704730545526e-2, (11, 5) = -0.2364269412330906e-2, (12, 1) = 1.5319805288911161, (12, 2) = 0.49724019908313965e-2, (12, 3) = -0.47113528942048085e-2, (12, 4) = 0.10660248274790495e-2, (12, 5) = -0.11153042237558037e-2, (13, 1) = 1.5345743659775581, (13, 2) = 0.24984995067600896e-2, (13, 3) = -0.2401250250975525e-2, (13, 4) = 0.5011966820226343e-3, (13, 5) = -0.5248289826886877e-3, (14, 1) = 1.5358728194208906, (14, 2) = 0.12440119569314578e-2, (14, 3) = -0.12093215573985628e-2, (14, 4) = 0.23544738145817105e-3, (14, 5) = -0.2466587850586314e-3, (15, 1) = 1.5365173102346918, (15, 2) = 0.6148015308811455e-3, (15, 3) = -0.6032811800317005e-3, (15, 4) = 0.11055525378085771e-3, (15, 5) = -0.11584628661588081e-3, (16, 1) = 1.536834972545, (16, 2) = 0.30197726796083954e-3, (16, 3) = -0.2986490288978108e-3, (16, 4) = 0.51899799851421e-4, (16, 5) = -0.5439103696428884e-4, (17, 1) = 1.5369906451774888, (17, 2) = 0.14755307935715694e-3, (17, 3) = -0.14690575453443246e-3, (17, 4) = 0.2436052045018883e-4, (17, 5) = -0.25532771206319318e-4, (18, 1) = 1.537066559314411, (18, 2) = 0.7177236700295585e-4, (18, 3) = -0.7187729398053743e-4, (18, 4) = 0.11432662628093271e-4, (18, 5) = -0.11984713858579463e-4, (19, 1) = 1.537103419510933, (19, 2) = 0.3477022315080817e-4, (19, 3) = -0.35007749994105596e-4, (19, 4) = 0.5364472172783753e-5, (19, 5) = -0.5625174866621487e-5, (20, 1) = 1.53712124655263, (20, 2) = 0.167801854213613e-4, (20, 3) = -0.16983543378325293e-4, (20, 4) = 0.2516289536316785e-5, (20, 5) = -0.2640190816045617e-5, (21, 1) = 1.5371298351182954, (21, 2) = 0.8066191186382534e-5, (21, 3) = -0.821104246872564e-5, (21, 4) = 0.11795051188684695e-5, (21, 5) = -0.12391870423047207e-5, (22, 1) = 1.537133955359844, (22, 2) = 0.3859180935593867e-5, (22, 3) = -0.395755789320176e-5, (22, 4) = 0.5520931946642665e-6, (22, 5) = -0.5816313926576407e-6, (23, 1) = 1.5371359212718083, (23, 2) = 0.18341823395610769e-5, (23, 3) = -0.19019345748834397e-5, (23, 4) = 0.2576175590429348e-6, (23, 5) = -0.2730071797956253e-6, (24, 1) = 1.5371368515706798, (24, 2) = 0.8623290091477282e-6, (24, 3) = -0.9113341483838946e-6, (24, 4) = 0.1194038808143948e-6, (24, 5) = -0.1281526473802194e-6, (25, 1) = 1.537137285591093, (25, 2) = 0.39734387332399116e-6, (25, 3) = -0.4351065480638164e-6, (25, 4) = 0.5452376150027097e-7, (25, 5) = -0.6015514998812785e-7, (26, 1) = 1.5371374825833801, (26, 2) = 0.17577216090080783e-6, (26, 3) = -0.2066547856380797e-6, (26, 4) = 0.24065480347840778e-7, (26, 5) = -0.2823339143989368e-7, (27, 1) = 1.5371375668997003, (27, 2) = 0.7087967992164601e-7, (27, 3) = -0.9729618184580756e-7, (27, 4) = 0.9768720688503002e-8, (27, 5) = -0.13249689734274169e-7, (28, 1) = 1.5371375980011175, (28, 2) = 0.2201947952838702e-7, (28, 3) = -0.45280562029436684e-7, (28, 4) = 0.30887065486698873e-8, (28, 5) = -0.6248707867260407e-8, (29, 1) = 1.537137604689266, (29, 2) = .0, (29, 3) = -0.20841183539706994e-7, (29, 4) = .0, (29, 5) = -0.30115916942592686e-8}, datatype = float[8], order = C_order); YP := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .9220907462515571, (1, 3) = -1.0, (1, 4) = -.38783340466369254, (1, 5) = .0, (2, 1) = .4202740870445161, (2, 2) = .3373570222677326, (2, 3) = -.6895707858708219, (2, 4) = -.37712948659838486, (2, 5) = 0.4303279115075219e-1, (3, 1) = .5163794040551701, (3, 2) = -0.19185064713216023e-1, (3, 3) = -.3511517120118227, (3, 4) = -.3229448930949884, (3, 5) = .11097150746096335, (4, 1) = .4417990492201716, (4, 2) = -.16651332416146195, (4, 3) = -0.9501085499656597e-1, (4, 4) = -.23454549848673548, (4, 5) = .13459484654365939, (5, 1) = .31549674554502644, (5, 2) = -.18074641710244985, (5, 3) = 0.3411652766552317e-1, (5, 4) = -.14708087178570156, (5, 5) = .11093836320508359, (6, 1) = .20118216105468362, (6, 2) = -.14047902635042844, (6, 3) = 0.6927210396491991e-1, (6, 4) = -0.8263424709324725e-1, (6, 5) = 0.7246495203970743e-1, (7, 1) = .11890906506576693, (7, 2) = -0.9294999327444896e-1, (7, 3) = 0.6122617103835701e-1, (7, 4) = -0.4313615270778873e-1, (7, 5) = 0.4110148141424317e-1, (8, 1) = 0.6667910031326235e-1, (8, 2) = -0.5593040786446294e-1, (8, 3) = 0.42483062663230695e-1, (8, 4) = -0.2150725154063105e-1, (8, 5) = 0.21439202918624025e-1, (9, 1) = 0.3603568604801351e-1, (9, 2) = -0.3167753384430381e-1, (9, 3) = 0.26135864069716998e-1, (9, 4) = -0.10438939815596704e-1, (9, 5) = 0.10660108900785871e-1, (10, 1) = 0.18960327498140035e-1, (10, 2) = -0.1722319045196687e-1, (10, 3) = 0.14980312940540426e-1, (10, 4) = -0.4988937027048127e-2, (10, 5) = 0.5159686682556715e-2, (11, 1) = 0.9782165431635105e-2, (11, 2) = -0.910157017546314e-2, (11, 3) = 0.820665675837047e-2, (11, 4) = -0.2364269412330906e-2, (11, 5) = 0.24612927413180455e-2, (12, 1) = 0.49724019908313965e-2, (12, 2) = -0.47113528942048085e-2, (12, 3) = 0.4359613237292593e-2, (12, 4) = -0.11153042237558037e-2, (12, 5) = 0.11649711508526675e-2, (13, 1) = 0.24984995067600896e-2, (13, 2) = -0.2401250250975525e-2, (13, 3) = 0.22655973789531695e-2, (13, 4) = -0.5248289826886877e-3, (13, 5) = 0.549128934106459e-3, (14, 1) = 0.12440119569314578e-2, (14, 2) = -0.12093215573985628e-2, (14, 3) = 0.11583494838774682e-2, (14, 4) = -0.2466587850586314e-3, (14, 5) = 0.2582976297565444e-3, (15, 1) = 0.6148015308811455e-3, (15, 2) = -0.6032811800317005e-3, (15, 3) = 0.5848477187234688e-3, (15, 4) = -0.11584628661588081e-3, (15, 5) = 0.12136351684889346e-3, (16, 1) = 0.30197726796083954e-3, (16, 2) = -0.2986490288978108e-3, (16, 3) = 0.29237649937883e-3, (16, 4) = -0.5439103696428884e-4, (16, 5) = 0.56993214408891095e-4, (17, 1) = 0.14755307935715694e-3, (17, 2) = -0.14690575453443246e-3, (17, 3) = 0.14499494333704743e-3, (17, 4) = -0.25532771206319318e-4, (17, 5) = 0.2675702078834315e-4, (18, 1) = 0.7177236700295585e-4, (18, 2) = -0.7187729398053743e-4, (18, 3) = 0.7143005172186065e-4, (18, 4) = -0.11984713858579463e-4, (18, 5) = 0.1255997924657351e-4, (19, 1) = 0.3477022315080817e-4, (19, 2) = -0.35007749994105596e-4, (19, 3) = 0.3499403148041789e-4, (19, 4) = -0.5625174866621487e-5, (19, 5) = 0.589532422011194e-5, (20, 1) = 0.167801854213613e-4, (20, 2) = -0.16983543378325293e-4, (20, 3) = 0.17063175277423634e-4, (20, 4) = -0.2640190816045617e-5, (20, 5) = 0.27670182261114854e-5, (21, 1) = 0.8066191186382534e-5, (21, 2) = -0.821104246872564e-5, (21, 3) = 0.828660617992783e-5, (21, 4) = -0.12391870423047207e-5, (21, 5) = 0.12987213913763072e-5, (22, 1) = 0.3859180935593867e-5, (22, 2) = -0.395755789320176e-5, (22, 3) = 0.4010386715431575e-5, (22, 4) = -0.5816313926576407e-6, (22, 5) = 0.6095763839708823e-6, (23, 1) = 0.18341823395610769e-5, (23, 2) = -0.19019345748834397e-5, (23, 3) = 0.19350330892911135e-5, (23, 4) = -0.2730071797956253e-6, (23, 5) = 0.28612441556520465e-6, (24, 1) = 0.8623290091477282e-6, (24, 2) = -0.9113341483838946e-6, (24, 3) = 0.931230468673015e-6, (24, 4) = -0.1281526473802194e-6, (24, 5) = 0.1343101069871441e-6, (25, 1) = 0.39734387332399116e-6, (25, 2) = -0.4351065480638164e-6, (25, 3) = 0.44709019111609976e-6, (25, 4) = -0.6015514998812785e-7, (25, 5) = 0.6304549361391542e-7, (26, 1) = 0.17577216090080783e-6, (26, 2) = -0.2066547856380797e-6, (26, 3) = 0.21417714781972993e-6, (26, 4) = -0.2823339143989368e-7, (26, 5) = 0.29589957438210912e-7, (27, 1) = 0.7087967992164601e-7, (27, 2) = -0.9729618184580756e-7, (27, 3) = 0.10239949399678307e-6, (27, 4) = -0.13249689734274169e-7, (27, 5) = 0.13886315345671458e-7, (28, 1) = 0.2201947952838702e-7, (28, 2) = -0.45280562029436684e-7, (28, 3) = 0.4911313445931053e-7, (28, 4) = -0.6248707867260407e-8, (28, 5) = 0.6548948046607739e-8, (29, 1) = .0, (29, 2) = -0.20841183539706994e-7, (29, 3) = 0.24026825208835925e-7, (29, 4) = -0.30115916942592686e-8, (29, 5) = 0.31562937567380326e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.947670133699624e-8, (1, 4) = .0, (1, 5) = -0.16801628863722625e-8, (2, 1) = -0.5562688680729497e-9, (2, 2) = -0.21544394426163097e-8, (2, 3) = 0.287293894307546e-8, (2, 4) = -0.37357656722536194e-8, (2, 5) = 0.32217191547761024e-8, (3, 1) = -0.8350526558565278e-8, (3, 2) = 0.4134830634172977e-8, (3, 3) = 0.12491061704911204e-8, (3, 4) = 0.3909918765623829e-8, (3, 5) = -0.20757291059677243e-9, (4, 1) = 0.16671389719705844e-9, (4, 2) = 0.3648160715899586e-8, (4, 3) = -0.528396986802508e-8, (4, 4) = 0.4823828777432993e-9, (4, 5) = -0.2408743014606509e-8, (5, 1) = 0.5571634668634835e-8, (5, 2) = -0.5437715786747662e-8, (5, 3) = 0.33059473772110423e-8, (5, 4) = -0.32522595808460493e-8, (5, 5) = 0.24277913015859777e-8, (6, 1) = -0.25669375582958455e-9, (6, 2) = -0.24447686990555343e-8, (6, 3) = 0.37763491733330965e-8, (6, 4) = 0.16312740125029958e-9, (6, 5) = 0.2836817825937946e-9, (7, 1) = -0.32389377868904443e-8, (7, 2) = 0.1881042655673872e-8, (7, 3) = -0.11396650576233194e-8, (7, 4) = 0.10620111323548136e-8, (7, 5) = -0.9612930708926523e-9, (8, 1) = -0.18812922832728336e-8, (8, 2) = 0.14232046751044453e-8, (8, 3) = -0.1537803668361072e-8, (8, 4) = 0.1770842620028042e-9, (8, 5) = -0.15945787869057221e-9, (9, 1) = -0.4702411602328281e-9, (9, 2) = 0.320333402872091e-11, (9, 3) = -0.9185162120441862e-10, (9, 4) = -0.19095599932287843e-9, (9, 5) = 0.23643248136766287e-9, (10, 1) = -0.17417744006906416e-9, (10, 2) = -0.4092039771380655e-9, (10, 3) = 0.4774557415611376e-9, (10, 4) = -0.11595631798509842e-9, (10, 5) = 0.14655938678934742e-9, (11, 1) = -0.36430615951141193e-9, (11, 2) = -0.22503070324966588e-9, (11, 3) = 0.31318800713246974e-9, (11, 4) = -0.7102340842716831e-11, (11, 5) = 0.14634454169986603e-10, (12, 1) = -0.5396388972588783e-9, (12, 2) = -0.10024023632452876e-10, (12, 3) = 0.52585615313555275e-10, (12, 4) = 0.30763893139739825e-10, (12, 5) = -0.34005653195770876e-10, (13, 1) = -0.5943567114066009e-9, (13, 2) = 0.7448998028657788e-10, (13, 3) = -0.708034730465589e-10, (13, 4) = 0.26507725195353555e-10, (13, 5) = -0.3134708409282319e-10, (14, 1) = -0.5789647343263283e-9, (14, 2) = 0.6946997649814925e-10, (14, 3) = -0.8160855192822036e-10, (14, 4) = 0.12965812897819388e-10, (14, 5) = -0.16205118685268952e-10, (15, 1) = -0.5480288674538708e-9, (15, 2) = 0.3755086868784173e-10, (15, 3) = -0.50490114989597235e-10, (15, 4) = 0.32350773786510558e-11, (15, 5) = -0.4700861305885854e-11, (16, 1) = -0.5257284342112479e-9, (16, 2) = 0.10919861164588246e-10, (16, 3) = -0.19346772632557297e-10, (16, 4) = -0.11790344440137198e-11, (16, 5) = 0.832624535476741e-12, (17, 1) = -0.5155200016654919e-9, (17, 2) = -0.30465560714292855e-11, (17, 3) = -0.8267473293057957e-12, (17, 4) = -0.22320654114644123e-11, (17, 5) = 0.2400655612059856e-11, (18, 1) = -0.5133923272616294e-9, (18, 2) = -0.737945441660333e-11, (18, 3) = 0.64527937509837154e-11, (18, 4) = -0.18460323317176304e-11, (18, 5) = 0.21645324044442117e-11, (19, 1) = -0.5148896773711696e-9, (19, 2) = -0.6805942618791494e-11, (19, 3) = 0.7290389637347693e-11, (19, 4) = -0.1127780748270535e-11, (19, 5) = 0.1426574333434267e-11, (20, 1) = -0.5172260423041393e-9, (20, 2) = -0.4657799114489725e-11, (20, 3) = 0.5567830559435603e-11, (20, 4) = -0.5303365272165861e-12, (20, 5) = 0.7538287303084591e-12, (21, 1) = -0.5191746746088076e-9, (21, 2) = -0.25874975582162318e-11, (21, 3) = 0.3436128045689803e-11, (21, 4) = -0.15574116810816628e-12, (21, 5) = 0.30144441341623344e-12, (22, 1) = -0.5204375227141072e-9, (22, 2) = -0.11365161545683807e-11, (22, 3) = 0.1752985745214996e-11, (22, 4) = 0.3249627740759922e-13, (22, 5) = 0.5150782611193112e-13, (23, 1) = -0.5211213531601294e-9, (23, 2) = -0.3082774300480712e-12, (23, 3) = 0.6809547502858554e-12, (23, 4) = 0.10140915458196715e-12, (23, 5) = -0.6050324746005763e-13, (24, 1) = -0.5214281864248747e-9, (24, 2) = 0.7242912386800786e-13, (24, 3) = 0.10576899938353571e-12, (24, 4) = 0.1072206483365034e-12, (24, 5) = -0.9414790219756612e-13, (25, 1) = -0.5215366608792588e-9, (25, 2) = 0.1891469519098857e-12, (25, 3) = -0.14497650859163652e-12, (25, 4) = 0.8641875813257649e-13, (25, 5) = -0.9035857945464468e-13, (26, 1) = -0.5215615175319244e-9, (26, 2) = 0.17670718185401007e-12, (26, 3) = -0.2150167149653954e-12, (26, 4) = 0.5891552332814735e-13, (26, 5) = -0.7282784304094444e-13, (27, 1) = -0.5215650870134602e-9, (27, 2) = 0.11694313367520813e-12, (27, 3) = -0.20000655303758359e-12, (27, 4) = 0.3377761208360633e-13, (27, 5) = -0.53341189571616226e-13, (28, 1) = -0.521579349038632e-9, (28, 2) = 0.5209631819213893e-13, (28, 3) = -0.15467632068966293e-12, (28, 4) = 0.14064084565986249e-13, (28, 5) = -0.3672938482279342e-13, (29, 1) = -0.5216042456082603e-9, (29, 2) = .0, (29, 3) = -0.10651195375400426e-12, (29, 4) = .0, (29, 5) = -0.24309258949721638e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 29, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 29, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187987466566, (2) = 18446884187987467006, (3) = 18446884187987467270, (4) = 18446884187987467446, (5) = 18446884187987467622, (6) = 18446884187987467798}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else g := pointto(data[2][2]); return ('g')(y) end if end if; try res := solnproc(outpoint); res[2] catch: error  end try end proc, D(g) = proc (y) local res, data, solnproc, `D(g)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .9220907462515571, (1, 4) = 1.0, (1, 5) = -.38783340466369254, (2, 1) = .16735567649115993, (2, 2) = .4202740870445161, (2, 3) = .3373570222677326, (2, 4) = .7355419804808778, (2, 5) = -.37712948659838486, (3, 1) = .503981373982817, (3, 2) = .5163794040551701, (3, 3) = -0.19185064713216023e-1, (3, 4) = .49172724293359593, (3, 5) = -.3229448930949884, (4, 1) = .8416523710936388, (4, 2) = .4417990492201716, (4, 3) = -.16651332416146195, (4, 4) = .2977138055168734, (4, 5) = -.23454549848673548, (5, 1) = 1.1062594162789947, (5, 2) = .31549674554502644, (5, 3) = -.18074641710244985, (5, 4) = .1656168899679353, (5, 5) = -.14708087178570156, (6, 1) = 1.2861729052641508, (6, 2) = .20118216105468362, (6, 3) = -.14047902635042844, (6, 4) = 0.8647526508575375e-1, (6, 5) = -0.8263424709324725e-1, (7, 1) = 1.3974860750621676, (7, 2) = .11890906506576693, (7, 3) = -0.9294999327444896e-1, (7, 4) = 0.4326575279767381e-1, (7, 5) = -0.4313615270778873e-1, (8, 1) = 1.462026155282785, (8, 2) = 0.6667910031326235e-1, (8, 3) = -0.5593040786446294e-1, (8, 4) = 0.21068777926171442e-1, (8, 5) = -0.2150725154063105e-1, (9, 1) = 1.497740830391555, (9, 2) = 0.3603568604801351e-1, (9, 3) = -0.3167753384430381e-1, (9, 4) = 0.10096973148301623e-1, (9, 5) = -0.10438939815596704e-1, (10, 1) = 1.516864299292917, (10, 2) = 0.18960327498140035e-1, (10, 3) = -0.1722319045196687e-1, (10, 4) = 0.4793366106261327e-2, (10, 5) = -0.4988937027048127e-2, (11, 1) = 1.5268547661160343, (11, 2) = 0.9782165431635105e-2, (11, 3) = -0.910157017546314e-2, (11, 4) = 0.22637704730545526e-2, (11, 5) = -0.2364269412330906e-2, (12, 1) = 1.5319805288911161, (12, 2) = 0.49724019908313965e-2, (12, 3) = -0.47113528942048085e-2, (12, 4) = 0.10660248274790495e-2, (12, 5) = -0.11153042237558037e-2, (13, 1) = 1.5345743659775581, (13, 2) = 0.24984995067600896e-2, (13, 3) = -0.2401250250975525e-2, (13, 4) = 0.5011966820226343e-3, (13, 5) = -0.5248289826886877e-3, (14, 1) = 1.5358728194208906, (14, 2) = 0.12440119569314578e-2, (14, 3) = -0.12093215573985628e-2, (14, 4) = 0.23544738145817105e-3, (14, 5) = -0.2466587850586314e-3, (15, 1) = 1.5365173102346918, (15, 2) = 0.6148015308811455e-3, (15, 3) = -0.6032811800317005e-3, (15, 4) = 0.11055525378085771e-3, (15, 5) = -0.11584628661588081e-3, (16, 1) = 1.536834972545, (16, 2) = 0.30197726796083954e-3, (16, 3) = -0.2986490288978108e-3, (16, 4) = 0.51899799851421e-4, (16, 5) = -0.5439103696428884e-4, (17, 1) = 1.5369906451774888, (17, 2) = 0.14755307935715694e-3, (17, 3) = -0.14690575453443246e-3, (17, 4) = 0.2436052045018883e-4, (17, 5) = -0.25532771206319318e-4, (18, 1) = 1.537066559314411, (18, 2) = 0.7177236700295585e-4, (18, 3) = -0.7187729398053743e-4, (18, 4) = 0.11432662628093271e-4, (18, 5) = -0.11984713858579463e-4, (19, 1) = 1.537103419510933, (19, 2) = 0.3477022315080817e-4, (19, 3) = -0.35007749994105596e-4, (19, 4) = 0.5364472172783753e-5, (19, 5) = -0.5625174866621487e-5, (20, 1) = 1.53712124655263, (20, 2) = 0.167801854213613e-4, (20, 3) = -0.16983543378325293e-4, (20, 4) = 0.2516289536316785e-5, (20, 5) = -0.2640190816045617e-5, (21, 1) = 1.5371298351182954, (21, 2) = 0.8066191186382534e-5, (21, 3) = -0.821104246872564e-5, (21, 4) = 0.11795051188684695e-5, (21, 5) = -0.12391870423047207e-5, (22, 1) = 1.537133955359844, (22, 2) = 0.3859180935593867e-5, (22, 3) = -0.395755789320176e-5, (22, 4) = 0.5520931946642665e-6, (22, 5) = -0.5816313926576407e-6, (23, 1) = 1.5371359212718083, (23, 2) = 0.18341823395610769e-5, (23, 3) = -0.19019345748834397e-5, (23, 4) = 0.2576175590429348e-6, (23, 5) = -0.2730071797956253e-6, (24, 1) = 1.5371368515706798, (24, 2) = 0.8623290091477282e-6, (24, 3) = -0.9113341483838946e-6, (24, 4) = 0.1194038808143948e-6, (24, 5) = -0.1281526473802194e-6, (25, 1) = 1.537137285591093, (25, 2) = 0.39734387332399116e-6, (25, 3) = -0.4351065480638164e-6, (25, 4) = 0.5452376150027097e-7, (25, 5) = -0.6015514998812785e-7, (26, 1) = 1.5371374825833801, (26, 2) = 0.17577216090080783e-6, (26, 3) = -0.2066547856380797e-6, (26, 4) = 0.24065480347840778e-7, (26, 5) = -0.2823339143989368e-7, (27, 1) = 1.5371375668997003, (27, 2) = 0.7087967992164601e-7, (27, 3) = -0.9729618184580756e-7, (27, 4) = 0.9768720688503002e-8, (27, 5) = -0.13249689734274169e-7, (28, 1) = 1.5371375980011175, (28, 2) = 0.2201947952838702e-7, (28, 3) = -0.45280562029436684e-7, (28, 4) = 0.30887065486698873e-8, (28, 5) = -0.6248707867260407e-8, (29, 1) = 1.537137604689266, (29, 2) = .0, (29, 3) = -0.20841183539706994e-7, (29, 4) = .0, (29, 5) = -0.30115916942592686e-8}, datatype = float[8], order = C_order); YP := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .9220907462515571, (1, 3) = -1.0, (1, 4) = -.38783340466369254, (1, 5) = .0, (2, 1) = .4202740870445161, (2, 2) = .3373570222677326, (2, 3) = -.6895707858708219, (2, 4) = -.37712948659838486, (2, 5) = 0.4303279115075219e-1, (3, 1) = .5163794040551701, (3, 2) = -0.19185064713216023e-1, (3, 3) = -.3511517120118227, (3, 4) = -.3229448930949884, (3, 5) = .11097150746096335, (4, 1) = .4417990492201716, (4, 2) = -.16651332416146195, (4, 3) = -0.9501085499656597e-1, (4, 4) = -.23454549848673548, (4, 5) = .13459484654365939, (5, 1) = .31549674554502644, (5, 2) = -.18074641710244985, (5, 3) = 0.3411652766552317e-1, (5, 4) = -.14708087178570156, (5, 5) = .11093836320508359, (6, 1) = .20118216105468362, (6, 2) = -.14047902635042844, (6, 3) = 0.6927210396491991e-1, (6, 4) = -0.8263424709324725e-1, (6, 5) = 0.7246495203970743e-1, (7, 1) = .11890906506576693, (7, 2) = -0.9294999327444896e-1, (7, 3) = 0.6122617103835701e-1, (7, 4) = -0.4313615270778873e-1, (7, 5) = 0.4110148141424317e-1, (8, 1) = 0.6667910031326235e-1, (8, 2) = -0.5593040786446294e-1, (8, 3) = 0.42483062663230695e-1, (8, 4) = -0.2150725154063105e-1, (8, 5) = 0.21439202918624025e-1, (9, 1) = 0.3603568604801351e-1, (9, 2) = -0.3167753384430381e-1, (9, 3) = 0.26135864069716998e-1, (9, 4) = -0.10438939815596704e-1, (9, 5) = 0.10660108900785871e-1, (10, 1) = 0.18960327498140035e-1, (10, 2) = -0.1722319045196687e-1, (10, 3) = 0.14980312940540426e-1, (10, 4) = -0.4988937027048127e-2, (10, 5) = 0.5159686682556715e-2, (11, 1) = 0.9782165431635105e-2, (11, 2) = -0.910157017546314e-2, (11, 3) = 0.820665675837047e-2, (11, 4) = -0.2364269412330906e-2, (11, 5) = 0.24612927413180455e-2, (12, 1) = 0.49724019908313965e-2, (12, 2) = -0.47113528942048085e-2, (12, 3) = 0.4359613237292593e-2, (12, 4) = -0.11153042237558037e-2, (12, 5) = 0.11649711508526675e-2, (13, 1) = 0.24984995067600896e-2, (13, 2) = -0.2401250250975525e-2, (13, 3) = 0.22655973789531695e-2, (13, 4) = -0.5248289826886877e-3, (13, 5) = 0.549128934106459e-3, (14, 1) = 0.12440119569314578e-2, (14, 2) = -0.12093215573985628e-2, (14, 3) = 0.11583494838774682e-2, (14, 4) = -0.2466587850586314e-3, (14, 5) = 0.2582976297565444e-3, (15, 1) = 0.6148015308811455e-3, (15, 2) = -0.6032811800317005e-3, (15, 3) = 0.5848477187234688e-3, (15, 4) = -0.11584628661588081e-3, (15, 5) = 0.12136351684889346e-3, (16, 1) = 0.30197726796083954e-3, (16, 2) = -0.2986490288978108e-3, (16, 3) = 0.29237649937883e-3, (16, 4) = -0.5439103696428884e-4, (16, 5) = 0.56993214408891095e-4, (17, 1) = 0.14755307935715694e-3, (17, 2) = -0.14690575453443246e-3, (17, 3) = 0.14499494333704743e-3, (17, 4) = -0.25532771206319318e-4, (17, 5) = 0.2675702078834315e-4, (18, 1) = 0.7177236700295585e-4, (18, 2) = -0.7187729398053743e-4, (18, 3) = 0.7143005172186065e-4, (18, 4) = -0.11984713858579463e-4, (18, 5) = 0.1255997924657351e-4, (19, 1) = 0.3477022315080817e-4, (19, 2) = -0.35007749994105596e-4, (19, 3) = 0.3499403148041789e-4, (19, 4) = -0.5625174866621487e-5, (19, 5) = 0.589532422011194e-5, (20, 1) = 0.167801854213613e-4, (20, 2) = -0.16983543378325293e-4, (20, 3) = 0.17063175277423634e-4, (20, 4) = -0.2640190816045617e-5, (20, 5) = 0.27670182261114854e-5, (21, 1) = 0.8066191186382534e-5, (21, 2) = -0.821104246872564e-5, (21, 3) = 0.828660617992783e-5, (21, 4) = -0.12391870423047207e-5, (21, 5) = 0.12987213913763072e-5, (22, 1) = 0.3859180935593867e-5, (22, 2) = -0.395755789320176e-5, (22, 3) = 0.4010386715431575e-5, (22, 4) = -0.5816313926576407e-6, (22, 5) = 0.6095763839708823e-6, (23, 1) = 0.18341823395610769e-5, (23, 2) = -0.19019345748834397e-5, (23, 3) = 0.19350330892911135e-5, (23, 4) = -0.2730071797956253e-6, (23, 5) = 0.28612441556520465e-6, (24, 1) = 0.8623290091477282e-6, (24, 2) = -0.9113341483838946e-6, (24, 3) = 0.931230468673015e-6, (24, 4) = -0.1281526473802194e-6, (24, 5) = 0.1343101069871441e-6, (25, 1) = 0.39734387332399116e-6, (25, 2) = -0.4351065480638164e-6, (25, 3) = 0.44709019111609976e-6, (25, 4) = -0.6015514998812785e-7, (25, 5) = 0.6304549361391542e-7, (26, 1) = 0.17577216090080783e-6, (26, 2) = -0.2066547856380797e-6, (26, 3) = 0.21417714781972993e-6, (26, 4) = -0.2823339143989368e-7, (26, 5) = 0.29589957438210912e-7, (27, 1) = 0.7087967992164601e-7, (27, 2) = -0.9729618184580756e-7, (27, 3) = 0.10239949399678307e-6, (27, 4) = -0.13249689734274169e-7, (27, 5) = 0.13886315345671458e-7, (28, 1) = 0.2201947952838702e-7, (28, 2) = -0.45280562029436684e-7, (28, 3) = 0.4911313445931053e-7, (28, 4) = -0.6248707867260407e-8, (28, 5) = 0.6548948046607739e-8, (29, 1) = .0, (29, 2) = -0.20841183539706994e-7, (29, 3) = 0.24026825208835925e-7, (29, 4) = -0.30115916942592686e-8, (29, 5) = 0.31562937567380326e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.947670133699624e-8, (1, 4) = .0, (1, 5) = -0.16801628863722625e-8, (2, 1) = -0.5562688680729497e-9, (2, 2) = -0.21544394426163097e-8, (2, 3) = 0.287293894307546e-8, (2, 4) = -0.37357656722536194e-8, (2, 5) = 0.32217191547761024e-8, (3, 1) = -0.8350526558565278e-8, (3, 2) = 0.4134830634172977e-8, (3, 3) = 0.12491061704911204e-8, (3, 4) = 0.3909918765623829e-8, (3, 5) = -0.20757291059677243e-9, (4, 1) = 0.16671389719705844e-9, (4, 2) = 0.3648160715899586e-8, (4, 3) = -0.528396986802508e-8, (4, 4) = 0.4823828777432993e-9, (4, 5) = -0.2408743014606509e-8, (5, 1) = 0.5571634668634835e-8, (5, 2) = -0.5437715786747662e-8, (5, 3) = 0.33059473772110423e-8, (5, 4) = -0.32522595808460493e-8, (5, 5) = 0.24277913015859777e-8, (6, 1) = -0.25669375582958455e-9, (6, 2) = -0.24447686990555343e-8, (6, 3) = 0.37763491733330965e-8, (6, 4) = 0.16312740125029958e-9, (6, 5) = 0.2836817825937946e-9, (7, 1) = -0.32389377868904443e-8, (7, 2) = 0.1881042655673872e-8, (7, 3) = -0.11396650576233194e-8, (7, 4) = 0.10620111323548136e-8, (7, 5) = -0.9612930708926523e-9, (8, 1) = -0.18812922832728336e-8, (8, 2) = 0.14232046751044453e-8, (8, 3) = -0.1537803668361072e-8, (8, 4) = 0.1770842620028042e-9, (8, 5) = -0.15945787869057221e-9, (9, 1) = -0.4702411602328281e-9, (9, 2) = 0.320333402872091e-11, (9, 3) = -0.9185162120441862e-10, (9, 4) = -0.19095599932287843e-9, (9, 5) = 0.23643248136766287e-9, (10, 1) = -0.17417744006906416e-9, (10, 2) = -0.4092039771380655e-9, (10, 3) = 0.4774557415611376e-9, (10, 4) = -0.11595631798509842e-9, (10, 5) = 0.14655938678934742e-9, (11, 1) = -0.36430615951141193e-9, (11, 2) = -0.22503070324966588e-9, (11, 3) = 0.31318800713246974e-9, (11, 4) = -0.7102340842716831e-11, (11, 5) = 0.14634454169986603e-10, (12, 1) = -0.5396388972588783e-9, (12, 2) = -0.10024023632452876e-10, (12, 3) = 0.52585615313555275e-10, (12, 4) = 0.30763893139739825e-10, (12, 5) = -0.34005653195770876e-10, (13, 1) = -0.5943567114066009e-9, (13, 2) = 0.7448998028657788e-10, (13, 3) = -0.708034730465589e-10, (13, 4) = 0.26507725195353555e-10, (13, 5) = -0.3134708409282319e-10, (14, 1) = -0.5789647343263283e-9, (14, 2) = 0.6946997649814925e-10, (14, 3) = -0.8160855192822036e-10, (14, 4) = 0.12965812897819388e-10, (14, 5) = -0.16205118685268952e-10, (15, 1) = -0.5480288674538708e-9, (15, 2) = 0.3755086868784173e-10, (15, 3) = -0.50490114989597235e-10, (15, 4) = 0.32350773786510558e-11, (15, 5) = -0.4700861305885854e-11, (16, 1) = -0.5257284342112479e-9, (16, 2) = 0.10919861164588246e-10, (16, 3) = -0.19346772632557297e-10, (16, 4) = -0.11790344440137198e-11, (16, 5) = 0.832624535476741e-12, (17, 1) = -0.5155200016654919e-9, (17, 2) = -0.30465560714292855e-11, (17, 3) = -0.8267473293057957e-12, (17, 4) = -0.22320654114644123e-11, (17, 5) = 0.2400655612059856e-11, (18, 1) = -0.5133923272616294e-9, (18, 2) = -0.737945441660333e-11, (18, 3) = 0.64527937509837154e-11, (18, 4) = -0.18460323317176304e-11, (18, 5) = 0.21645324044442117e-11, (19, 1) = -0.5148896773711696e-9, (19, 2) = -0.6805942618791494e-11, (19, 3) = 0.7290389637347693e-11, (19, 4) = -0.1127780748270535e-11, (19, 5) = 0.1426574333434267e-11, (20, 1) = -0.5172260423041393e-9, (20, 2) = -0.4657799114489725e-11, (20, 3) = 0.5567830559435603e-11, (20, 4) = -0.5303365272165861e-12, (20, 5) = 0.7538287303084591e-12, (21, 1) = -0.5191746746088076e-9, (21, 2) = -0.25874975582162318e-11, (21, 3) = 0.3436128045689803e-11, (21, 4) = -0.15574116810816628e-12, (21, 5) = 0.30144441341623344e-12, (22, 1) = -0.5204375227141072e-9, (22, 2) = -0.11365161545683807e-11, (22, 3) = 0.1752985745214996e-11, (22, 4) = 0.3249627740759922e-13, (22, 5) = 0.5150782611193112e-13, (23, 1) = -0.5211213531601294e-9, (23, 2) = -0.3082774300480712e-12, (23, 3) = 0.6809547502858554e-12, (23, 4) = 0.10140915458196715e-12, (23, 5) = -0.6050324746005763e-13, (24, 1) = -0.5214281864248747e-9, (24, 2) = 0.7242912386800786e-13, (24, 3) = 0.10576899938353571e-12, (24, 4) = 0.1072206483365034e-12, (24, 5) = -0.9414790219756612e-13, (25, 1) = -0.5215366608792588e-9, (25, 2) = 0.1891469519098857e-12, (25, 3) = -0.14497650859163652e-12, (25, 4) = 0.8641875813257649e-13, (25, 5) = -0.9035857945464468e-13, (26, 1) = -0.5215615175319244e-9, (26, 2) = 0.17670718185401007e-12, (26, 3) = -0.2150167149653954e-12, (26, 4) = 0.5891552332814735e-13, (26, 5) = -0.7282784304094444e-13, (27, 1) = -0.5215650870134602e-9, (27, 2) = 0.11694313367520813e-12, (27, 3) = -0.20000655303758359e-12, (27, 4) = 0.3377761208360633e-13, (27, 5) = -0.53341189571616226e-13, (28, 1) = -0.521579349038632e-9, (28, 2) = 0.5209631819213893e-13, (28, 3) = -0.15467632068966293e-12, (28, 4) = 0.14064084565986249e-13, (28, 5) = -0.3672938482279342e-13, (29, 1) = -0.5216042456082603e-9, (29, 2) = .0, (29, 3) = -0.10651195375400426e-12, (29, 4) = .0, (29, 5) = -0.24309258949721638e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 29, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 29, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187987466566, (2) = 18446884187987467006, (3) = 18446884187987467270, (4) = 18446884187987467446, (5) = 18446884187987467622, (6) = 18446884187987467798}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `D(g)` := pointto(data[2][3]); return ('`D(g)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc, (D@@2)(g) = proc (y) local res, data, solnproc, `\`@@\`(D,2)(g)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .9220907462515571, (1, 4) = 1.0, (1, 5) = -.38783340466369254, (2, 1) = .16735567649115993, (2, 2) = .4202740870445161, (2, 3) = .3373570222677326, (2, 4) = .7355419804808778, (2, 5) = -.37712948659838486, (3, 1) = .503981373982817, (3, 2) = .5163794040551701, (3, 3) = -0.19185064713216023e-1, (3, 4) = .49172724293359593, (3, 5) = -.3229448930949884, (4, 1) = .8416523710936388, (4, 2) = .4417990492201716, (4, 3) = -.16651332416146195, (4, 4) = .2977138055168734, (4, 5) = -.23454549848673548, (5, 1) = 1.1062594162789947, (5, 2) = .31549674554502644, (5, 3) = -.18074641710244985, (5, 4) = .1656168899679353, (5, 5) = -.14708087178570156, (6, 1) = 1.2861729052641508, (6, 2) = .20118216105468362, (6, 3) = -.14047902635042844, (6, 4) = 0.8647526508575375e-1, (6, 5) = -0.8263424709324725e-1, (7, 1) = 1.3974860750621676, (7, 2) = .11890906506576693, (7, 3) = -0.9294999327444896e-1, (7, 4) = 0.4326575279767381e-1, (7, 5) = -0.4313615270778873e-1, (8, 1) = 1.462026155282785, (8, 2) = 0.6667910031326235e-1, (8, 3) = -0.5593040786446294e-1, (8, 4) = 0.21068777926171442e-1, (8, 5) = -0.2150725154063105e-1, (9, 1) = 1.497740830391555, (9, 2) = 0.3603568604801351e-1, (9, 3) = -0.3167753384430381e-1, (9, 4) = 0.10096973148301623e-1, (9, 5) = -0.10438939815596704e-1, (10, 1) = 1.516864299292917, (10, 2) = 0.18960327498140035e-1, (10, 3) = -0.1722319045196687e-1, (10, 4) = 0.4793366106261327e-2, (10, 5) = -0.4988937027048127e-2, (11, 1) = 1.5268547661160343, (11, 2) = 0.9782165431635105e-2, (11, 3) = -0.910157017546314e-2, (11, 4) = 0.22637704730545526e-2, (11, 5) = -0.2364269412330906e-2, (12, 1) = 1.5319805288911161, (12, 2) = 0.49724019908313965e-2, (12, 3) = -0.47113528942048085e-2, (12, 4) = 0.10660248274790495e-2, (12, 5) = -0.11153042237558037e-2, (13, 1) = 1.5345743659775581, (13, 2) = 0.24984995067600896e-2, (13, 3) = -0.2401250250975525e-2, (13, 4) = 0.5011966820226343e-3, (13, 5) = -0.5248289826886877e-3, (14, 1) = 1.5358728194208906, (14, 2) = 0.12440119569314578e-2, (14, 3) = -0.12093215573985628e-2, (14, 4) = 0.23544738145817105e-3, (14, 5) = -0.2466587850586314e-3, (15, 1) = 1.5365173102346918, (15, 2) = 0.6148015308811455e-3, (15, 3) = -0.6032811800317005e-3, (15, 4) = 0.11055525378085771e-3, (15, 5) = -0.11584628661588081e-3, (16, 1) = 1.536834972545, (16, 2) = 0.30197726796083954e-3, (16, 3) = -0.2986490288978108e-3, (16, 4) = 0.51899799851421e-4, (16, 5) = -0.5439103696428884e-4, (17, 1) = 1.5369906451774888, (17, 2) = 0.14755307935715694e-3, (17, 3) = -0.14690575453443246e-3, (17, 4) = 0.2436052045018883e-4, (17, 5) = -0.25532771206319318e-4, (18, 1) = 1.537066559314411, (18, 2) = 0.7177236700295585e-4, (18, 3) = -0.7187729398053743e-4, (18, 4) = 0.11432662628093271e-4, (18, 5) = -0.11984713858579463e-4, (19, 1) = 1.537103419510933, (19, 2) = 0.3477022315080817e-4, (19, 3) = -0.35007749994105596e-4, (19, 4) = 0.5364472172783753e-5, (19, 5) = -0.5625174866621487e-5, (20, 1) = 1.53712124655263, (20, 2) = 0.167801854213613e-4, (20, 3) = -0.16983543378325293e-4, (20, 4) = 0.2516289536316785e-5, (20, 5) = -0.2640190816045617e-5, (21, 1) = 1.5371298351182954, (21, 2) = 0.8066191186382534e-5, (21, 3) = -0.821104246872564e-5, (21, 4) = 0.11795051188684695e-5, (21, 5) = -0.12391870423047207e-5, (22, 1) = 1.537133955359844, (22, 2) = 0.3859180935593867e-5, (22, 3) = -0.395755789320176e-5, (22, 4) = 0.5520931946642665e-6, (22, 5) = -0.5816313926576407e-6, (23, 1) = 1.5371359212718083, (23, 2) = 0.18341823395610769e-5, (23, 3) = -0.19019345748834397e-5, (23, 4) = 0.2576175590429348e-6, (23, 5) = -0.2730071797956253e-6, (24, 1) = 1.5371368515706798, (24, 2) = 0.8623290091477282e-6, (24, 3) = -0.9113341483838946e-6, (24, 4) = 0.1194038808143948e-6, (24, 5) = -0.1281526473802194e-6, (25, 1) = 1.537137285591093, (25, 2) = 0.39734387332399116e-6, (25, 3) = -0.4351065480638164e-6, (25, 4) = 0.5452376150027097e-7, (25, 5) = -0.6015514998812785e-7, (26, 1) = 1.5371374825833801, (26, 2) = 0.17577216090080783e-6, (26, 3) = -0.2066547856380797e-6, (26, 4) = 0.24065480347840778e-7, (26, 5) = -0.2823339143989368e-7, (27, 1) = 1.5371375668997003, (27, 2) = 0.7087967992164601e-7, (27, 3) = -0.9729618184580756e-7, (27, 4) = 0.9768720688503002e-8, (27, 5) = -0.13249689734274169e-7, (28, 1) = 1.5371375980011175, (28, 2) = 0.2201947952838702e-7, (28, 3) = -0.45280562029436684e-7, (28, 4) = 0.30887065486698873e-8, (28, 5) = -0.6248707867260407e-8, (29, 1) = 1.537137604689266, (29, 2) = .0, (29, 3) = -0.20841183539706994e-7, (29, 4) = .0, (29, 5) = -0.30115916942592686e-8}, datatype = float[8], order = C_order); YP := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .9220907462515571, (1, 3) = -1.0, (1, 4) = -.38783340466369254, (1, 5) = .0, (2, 1) = .4202740870445161, (2, 2) = .3373570222677326, (2, 3) = -.6895707858708219, (2, 4) = -.37712948659838486, (2, 5) = 0.4303279115075219e-1, (3, 1) = .5163794040551701, (3, 2) = -0.19185064713216023e-1, (3, 3) = -.3511517120118227, (3, 4) = -.3229448930949884, (3, 5) = .11097150746096335, (4, 1) = .4417990492201716, (4, 2) = -.16651332416146195, (4, 3) = -0.9501085499656597e-1, (4, 4) = -.23454549848673548, (4, 5) = .13459484654365939, (5, 1) = .31549674554502644, (5, 2) = -.18074641710244985, (5, 3) = 0.3411652766552317e-1, (5, 4) = -.14708087178570156, (5, 5) = .11093836320508359, (6, 1) = .20118216105468362, (6, 2) = -.14047902635042844, (6, 3) = 0.6927210396491991e-1, (6, 4) = -0.8263424709324725e-1, (6, 5) = 0.7246495203970743e-1, (7, 1) = .11890906506576693, (7, 2) = -0.9294999327444896e-1, (7, 3) = 0.6122617103835701e-1, (7, 4) = -0.4313615270778873e-1, (7, 5) = 0.4110148141424317e-1, (8, 1) = 0.6667910031326235e-1, (8, 2) = -0.5593040786446294e-1, (8, 3) = 0.42483062663230695e-1, (8, 4) = -0.2150725154063105e-1, (8, 5) = 0.21439202918624025e-1, (9, 1) = 0.3603568604801351e-1, (9, 2) = -0.3167753384430381e-1, (9, 3) = 0.26135864069716998e-1, (9, 4) = -0.10438939815596704e-1, (9, 5) = 0.10660108900785871e-1, (10, 1) = 0.18960327498140035e-1, (10, 2) = -0.1722319045196687e-1, (10, 3) = 0.14980312940540426e-1, (10, 4) = -0.4988937027048127e-2, (10, 5) = 0.5159686682556715e-2, (11, 1) = 0.9782165431635105e-2, (11, 2) = -0.910157017546314e-2, (11, 3) = 0.820665675837047e-2, (11, 4) = -0.2364269412330906e-2, (11, 5) = 0.24612927413180455e-2, (12, 1) = 0.49724019908313965e-2, (12, 2) = -0.47113528942048085e-2, (12, 3) = 0.4359613237292593e-2, (12, 4) = -0.11153042237558037e-2, (12, 5) = 0.11649711508526675e-2, (13, 1) = 0.24984995067600896e-2, (13, 2) = -0.2401250250975525e-2, (13, 3) = 0.22655973789531695e-2, (13, 4) = -0.5248289826886877e-3, (13, 5) = 0.549128934106459e-3, (14, 1) = 0.12440119569314578e-2, (14, 2) = -0.12093215573985628e-2, (14, 3) = 0.11583494838774682e-2, (14, 4) = -0.2466587850586314e-3, (14, 5) = 0.2582976297565444e-3, (15, 1) = 0.6148015308811455e-3, (15, 2) = -0.6032811800317005e-3, (15, 3) = 0.5848477187234688e-3, (15, 4) = -0.11584628661588081e-3, (15, 5) = 0.12136351684889346e-3, (16, 1) = 0.30197726796083954e-3, (16, 2) = -0.2986490288978108e-3, (16, 3) = 0.29237649937883e-3, (16, 4) = -0.5439103696428884e-4, (16, 5) = 0.56993214408891095e-4, (17, 1) = 0.14755307935715694e-3, (17, 2) = -0.14690575453443246e-3, (17, 3) = 0.14499494333704743e-3, (17, 4) = -0.25532771206319318e-4, (17, 5) = 0.2675702078834315e-4, (18, 1) = 0.7177236700295585e-4, (18, 2) = -0.7187729398053743e-4, (18, 3) = 0.7143005172186065e-4, (18, 4) = -0.11984713858579463e-4, (18, 5) = 0.1255997924657351e-4, (19, 1) = 0.3477022315080817e-4, (19, 2) = -0.35007749994105596e-4, (19, 3) = 0.3499403148041789e-4, (19, 4) = -0.5625174866621487e-5, (19, 5) = 0.589532422011194e-5, (20, 1) = 0.167801854213613e-4, (20, 2) = -0.16983543378325293e-4, (20, 3) = 0.17063175277423634e-4, (20, 4) = -0.2640190816045617e-5, (20, 5) = 0.27670182261114854e-5, (21, 1) = 0.8066191186382534e-5, (21, 2) = -0.821104246872564e-5, (21, 3) = 0.828660617992783e-5, (21, 4) = -0.12391870423047207e-5, (21, 5) = 0.12987213913763072e-5, (22, 1) = 0.3859180935593867e-5, (22, 2) = -0.395755789320176e-5, (22, 3) = 0.4010386715431575e-5, (22, 4) = -0.5816313926576407e-6, (22, 5) = 0.6095763839708823e-6, (23, 1) = 0.18341823395610769e-5, (23, 2) = -0.19019345748834397e-5, (23, 3) = 0.19350330892911135e-5, (23, 4) = -0.2730071797956253e-6, (23, 5) = 0.28612441556520465e-6, (24, 1) = 0.8623290091477282e-6, (24, 2) = -0.9113341483838946e-6, (24, 3) = 0.931230468673015e-6, (24, 4) = -0.1281526473802194e-6, (24, 5) = 0.1343101069871441e-6, (25, 1) = 0.39734387332399116e-6, (25, 2) = -0.4351065480638164e-6, (25, 3) = 0.44709019111609976e-6, (25, 4) = -0.6015514998812785e-7, (25, 5) = 0.6304549361391542e-7, (26, 1) = 0.17577216090080783e-6, (26, 2) = -0.2066547856380797e-6, (26, 3) = 0.21417714781972993e-6, (26, 4) = -0.2823339143989368e-7, (26, 5) = 0.29589957438210912e-7, (27, 1) = 0.7087967992164601e-7, (27, 2) = -0.9729618184580756e-7, (27, 3) = 0.10239949399678307e-6, (27, 4) = -0.13249689734274169e-7, (27, 5) = 0.13886315345671458e-7, (28, 1) = 0.2201947952838702e-7, (28, 2) = -0.45280562029436684e-7, (28, 3) = 0.4911313445931053e-7, (28, 4) = -0.6248707867260407e-8, (28, 5) = 0.6548948046607739e-8, (29, 1) = .0, (29, 2) = -0.20841183539706994e-7, (29, 3) = 0.24026825208835925e-7, (29, 4) = -0.30115916942592686e-8, (29, 5) = 0.31562937567380326e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.947670133699624e-8, (1, 4) = .0, (1, 5) = -0.16801628863722625e-8, (2, 1) = -0.5562688680729497e-9, (2, 2) = -0.21544394426163097e-8, (2, 3) = 0.287293894307546e-8, (2, 4) = -0.37357656722536194e-8, (2, 5) = 0.32217191547761024e-8, (3, 1) = -0.8350526558565278e-8, (3, 2) = 0.4134830634172977e-8, (3, 3) = 0.12491061704911204e-8, (3, 4) = 0.3909918765623829e-8, (3, 5) = -0.20757291059677243e-9, (4, 1) = 0.16671389719705844e-9, (4, 2) = 0.3648160715899586e-8, (4, 3) = -0.528396986802508e-8, (4, 4) = 0.4823828777432993e-9, (4, 5) = -0.2408743014606509e-8, (5, 1) = 0.5571634668634835e-8, (5, 2) = -0.5437715786747662e-8, (5, 3) = 0.33059473772110423e-8, (5, 4) = -0.32522595808460493e-8, (5, 5) = 0.24277913015859777e-8, (6, 1) = -0.25669375582958455e-9, (6, 2) = -0.24447686990555343e-8, (6, 3) = 0.37763491733330965e-8, (6, 4) = 0.16312740125029958e-9, (6, 5) = 0.2836817825937946e-9, (7, 1) = -0.32389377868904443e-8, (7, 2) = 0.1881042655673872e-8, (7, 3) = -0.11396650576233194e-8, (7, 4) = 0.10620111323548136e-8, (7, 5) = -0.9612930708926523e-9, (8, 1) = -0.18812922832728336e-8, (8, 2) = 0.14232046751044453e-8, (8, 3) = -0.1537803668361072e-8, (8, 4) = 0.1770842620028042e-9, (8, 5) = -0.15945787869057221e-9, (9, 1) = -0.4702411602328281e-9, (9, 2) = 0.320333402872091e-11, (9, 3) = -0.9185162120441862e-10, (9, 4) = -0.19095599932287843e-9, (9, 5) = 0.23643248136766287e-9, (10, 1) = -0.17417744006906416e-9, (10, 2) = -0.4092039771380655e-9, (10, 3) = 0.4774557415611376e-9, (10, 4) = -0.11595631798509842e-9, (10, 5) = 0.14655938678934742e-9, (11, 1) = -0.36430615951141193e-9, (11, 2) = -0.22503070324966588e-9, (11, 3) = 0.31318800713246974e-9, (11, 4) = -0.7102340842716831e-11, (11, 5) = 0.14634454169986603e-10, (12, 1) = -0.5396388972588783e-9, (12, 2) = -0.10024023632452876e-10, (12, 3) = 0.52585615313555275e-10, (12, 4) = 0.30763893139739825e-10, (12, 5) = -0.34005653195770876e-10, (13, 1) = -0.5943567114066009e-9, (13, 2) = 0.7448998028657788e-10, (13, 3) = -0.708034730465589e-10, (13, 4) = 0.26507725195353555e-10, (13, 5) = -0.3134708409282319e-10, (14, 1) = -0.5789647343263283e-9, (14, 2) = 0.6946997649814925e-10, (14, 3) = -0.8160855192822036e-10, (14, 4) = 0.12965812897819388e-10, (14, 5) = -0.16205118685268952e-10, (15, 1) = -0.5480288674538708e-9, (15, 2) = 0.3755086868784173e-10, (15, 3) = -0.50490114989597235e-10, (15, 4) = 0.32350773786510558e-11, (15, 5) = -0.4700861305885854e-11, (16, 1) = -0.5257284342112479e-9, (16, 2) = 0.10919861164588246e-10, (16, 3) = -0.19346772632557297e-10, (16, 4) = -0.11790344440137198e-11, (16, 5) = 0.832624535476741e-12, (17, 1) = -0.5155200016654919e-9, (17, 2) = -0.30465560714292855e-11, (17, 3) = -0.8267473293057957e-12, (17, 4) = -0.22320654114644123e-11, (17, 5) = 0.2400655612059856e-11, (18, 1) = -0.5133923272616294e-9, (18, 2) = -0.737945441660333e-11, (18, 3) = 0.64527937509837154e-11, (18, 4) = -0.18460323317176304e-11, (18, 5) = 0.21645324044442117e-11, (19, 1) = -0.5148896773711696e-9, (19, 2) = -0.6805942618791494e-11, (19, 3) = 0.7290389637347693e-11, (19, 4) = -0.1127780748270535e-11, (19, 5) = 0.1426574333434267e-11, (20, 1) = -0.5172260423041393e-9, (20, 2) = -0.4657799114489725e-11, (20, 3) = 0.5567830559435603e-11, (20, 4) = -0.5303365272165861e-12, (20, 5) = 0.7538287303084591e-12, (21, 1) = -0.5191746746088076e-9, (21, 2) = -0.25874975582162318e-11, (21, 3) = 0.3436128045689803e-11, (21, 4) = -0.15574116810816628e-12, (21, 5) = 0.30144441341623344e-12, (22, 1) = -0.5204375227141072e-9, (22, 2) = -0.11365161545683807e-11, (22, 3) = 0.1752985745214996e-11, (22, 4) = 0.3249627740759922e-13, (22, 5) = 0.5150782611193112e-13, (23, 1) = -0.5211213531601294e-9, (23, 2) = -0.3082774300480712e-12, (23, 3) = 0.6809547502858554e-12, (23, 4) = 0.10140915458196715e-12, (23, 5) = -0.6050324746005763e-13, (24, 1) = -0.5214281864248747e-9, (24, 2) = 0.7242912386800786e-13, (24, 3) = 0.10576899938353571e-12, (24, 4) = 0.1072206483365034e-12, (24, 5) = -0.9414790219756612e-13, (25, 1) = -0.5215366608792588e-9, (25, 2) = 0.1891469519098857e-12, (25, 3) = -0.14497650859163652e-12, (25, 4) = 0.8641875813257649e-13, (25, 5) = -0.9035857945464468e-13, (26, 1) = -0.5215615175319244e-9, (26, 2) = 0.17670718185401007e-12, (26, 3) = -0.2150167149653954e-12, (26, 4) = 0.5891552332814735e-13, (26, 5) = -0.7282784304094444e-13, (27, 1) = -0.5215650870134602e-9, (27, 2) = 0.11694313367520813e-12, (27, 3) = -0.20000655303758359e-12, (27, 4) = 0.3377761208360633e-13, (27, 5) = -0.53341189571616226e-13, (28, 1) = -0.521579349038632e-9, (28, 2) = 0.5209631819213893e-13, (28, 3) = -0.15467632068966293e-12, (28, 4) = 0.14064084565986249e-13, (28, 5) = -0.3672938482279342e-13, (29, 1) = -0.5216042456082603e-9, (29, 2) = .0, (29, 3) = -0.10651195375400426e-12, (29, 4) = .0, (29, 5) = -0.24309258949721638e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 29, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 29, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187987466566, (2) = 18446884187987467006, (3) = 18446884187987467270, (4) = 18446884187987467446, (5) = 18446884187987467622, (6) = 18446884187987467798}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `\`@@\`(D,2)(g)` := pointto(data[2][4]); return ('`\`@@\`(D,2)(g)`')(y) end if end if; try res := solnproc(outpoint); res[4] catch: error  end try end proc, h = proc (y) local res, data, solnproc, h, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .9220907462515571, (1, 4) = 1.0, (1, 5) = -.38783340466369254, (2, 1) = .16735567649115993, (2, 2) = .4202740870445161, (2, 3) = .3373570222677326, (2, 4) = .7355419804808778, (2, 5) = -.37712948659838486, (3, 1) = .503981373982817, (3, 2) = .5163794040551701, (3, 3) = -0.19185064713216023e-1, (3, 4) = .49172724293359593, (3, 5) = -.3229448930949884, (4, 1) = .8416523710936388, (4, 2) = .4417990492201716, (4, 3) = -.16651332416146195, (4, 4) = .2977138055168734, (4, 5) = -.23454549848673548, (5, 1) = 1.1062594162789947, (5, 2) = .31549674554502644, (5, 3) = -.18074641710244985, (5, 4) = .1656168899679353, (5, 5) = -.14708087178570156, (6, 1) = 1.2861729052641508, (6, 2) = .20118216105468362, (6, 3) = -.14047902635042844, (6, 4) = 0.8647526508575375e-1, (6, 5) = -0.8263424709324725e-1, (7, 1) = 1.3974860750621676, (7, 2) = .11890906506576693, (7, 3) = -0.9294999327444896e-1, (7, 4) = 0.4326575279767381e-1, (7, 5) = -0.4313615270778873e-1, (8, 1) = 1.462026155282785, (8, 2) = 0.6667910031326235e-1, (8, 3) = -0.5593040786446294e-1, (8, 4) = 0.21068777926171442e-1, (8, 5) = -0.2150725154063105e-1, (9, 1) = 1.497740830391555, (9, 2) = 0.3603568604801351e-1, (9, 3) = -0.3167753384430381e-1, (9, 4) = 0.10096973148301623e-1, (9, 5) = -0.10438939815596704e-1, (10, 1) = 1.516864299292917, (10, 2) = 0.18960327498140035e-1, (10, 3) = -0.1722319045196687e-1, (10, 4) = 0.4793366106261327e-2, (10, 5) = -0.4988937027048127e-2, (11, 1) = 1.5268547661160343, (11, 2) = 0.9782165431635105e-2, (11, 3) = -0.910157017546314e-2, (11, 4) = 0.22637704730545526e-2, (11, 5) = -0.2364269412330906e-2, (12, 1) = 1.5319805288911161, (12, 2) = 0.49724019908313965e-2, (12, 3) = -0.47113528942048085e-2, (12, 4) = 0.10660248274790495e-2, (12, 5) = -0.11153042237558037e-2, (13, 1) = 1.5345743659775581, (13, 2) = 0.24984995067600896e-2, (13, 3) = -0.2401250250975525e-2, (13, 4) = 0.5011966820226343e-3, (13, 5) = -0.5248289826886877e-3, (14, 1) = 1.5358728194208906, (14, 2) = 0.12440119569314578e-2, (14, 3) = -0.12093215573985628e-2, (14, 4) = 0.23544738145817105e-3, (14, 5) = -0.2466587850586314e-3, (15, 1) = 1.5365173102346918, (15, 2) = 0.6148015308811455e-3, (15, 3) = -0.6032811800317005e-3, (15, 4) = 0.11055525378085771e-3, (15, 5) = -0.11584628661588081e-3, (16, 1) = 1.536834972545, (16, 2) = 0.30197726796083954e-3, (16, 3) = -0.2986490288978108e-3, (16, 4) = 0.51899799851421e-4, (16, 5) = -0.5439103696428884e-4, (17, 1) = 1.5369906451774888, (17, 2) = 0.14755307935715694e-3, (17, 3) = -0.14690575453443246e-3, (17, 4) = 0.2436052045018883e-4, (17, 5) = -0.25532771206319318e-4, (18, 1) = 1.537066559314411, (18, 2) = 0.7177236700295585e-4, (18, 3) = -0.7187729398053743e-4, (18, 4) = 0.11432662628093271e-4, (18, 5) = -0.11984713858579463e-4, (19, 1) = 1.537103419510933, (19, 2) = 0.3477022315080817e-4, (19, 3) = -0.35007749994105596e-4, (19, 4) = 0.5364472172783753e-5, (19, 5) = -0.5625174866621487e-5, (20, 1) = 1.53712124655263, (20, 2) = 0.167801854213613e-4, (20, 3) = -0.16983543378325293e-4, (20, 4) = 0.2516289536316785e-5, (20, 5) = -0.2640190816045617e-5, (21, 1) = 1.5371298351182954, (21, 2) = 0.8066191186382534e-5, (21, 3) = -0.821104246872564e-5, (21, 4) = 0.11795051188684695e-5, (21, 5) = -0.12391870423047207e-5, (22, 1) = 1.537133955359844, (22, 2) = 0.3859180935593867e-5, (22, 3) = -0.395755789320176e-5, (22, 4) = 0.5520931946642665e-6, (22, 5) = -0.5816313926576407e-6, (23, 1) = 1.5371359212718083, (23, 2) = 0.18341823395610769e-5, (23, 3) = -0.19019345748834397e-5, (23, 4) = 0.2576175590429348e-6, (23, 5) = -0.2730071797956253e-6, (24, 1) = 1.5371368515706798, (24, 2) = 0.8623290091477282e-6, (24, 3) = -0.9113341483838946e-6, (24, 4) = 0.1194038808143948e-6, (24, 5) = -0.1281526473802194e-6, (25, 1) = 1.537137285591093, (25, 2) = 0.39734387332399116e-6, (25, 3) = -0.4351065480638164e-6, (25, 4) = 0.5452376150027097e-7, (25, 5) = -0.6015514998812785e-7, (26, 1) = 1.5371374825833801, (26, 2) = 0.17577216090080783e-6, (26, 3) = -0.2066547856380797e-6, (26, 4) = 0.24065480347840778e-7, (26, 5) = -0.2823339143989368e-7, (27, 1) = 1.5371375668997003, (27, 2) = 0.7087967992164601e-7, (27, 3) = -0.9729618184580756e-7, (27, 4) = 0.9768720688503002e-8, (27, 5) = -0.13249689734274169e-7, (28, 1) = 1.5371375980011175, (28, 2) = 0.2201947952838702e-7, (28, 3) = -0.45280562029436684e-7, (28, 4) = 0.30887065486698873e-8, (28, 5) = -0.6248707867260407e-8, (29, 1) = 1.537137604689266, (29, 2) = .0, (29, 3) = -0.20841183539706994e-7, (29, 4) = .0, (29, 5) = -0.30115916942592686e-8}, datatype = float[8], order = C_order); YP := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .9220907462515571, (1, 3) = -1.0, (1, 4) = -.38783340466369254, (1, 5) = .0, (2, 1) = .4202740870445161, (2, 2) = .3373570222677326, (2, 3) = -.6895707858708219, (2, 4) = -.37712948659838486, (2, 5) = 0.4303279115075219e-1, (3, 1) = .5163794040551701, (3, 2) = -0.19185064713216023e-1, (3, 3) = -.3511517120118227, (3, 4) = -.3229448930949884, (3, 5) = .11097150746096335, (4, 1) = .4417990492201716, (4, 2) = -.16651332416146195, (4, 3) = -0.9501085499656597e-1, (4, 4) = -.23454549848673548, (4, 5) = .13459484654365939, (5, 1) = .31549674554502644, (5, 2) = -.18074641710244985, (5, 3) = 0.3411652766552317e-1, (5, 4) = -.14708087178570156, (5, 5) = .11093836320508359, (6, 1) = .20118216105468362, (6, 2) = -.14047902635042844, (6, 3) = 0.6927210396491991e-1, (6, 4) = -0.8263424709324725e-1, (6, 5) = 0.7246495203970743e-1, (7, 1) = .11890906506576693, (7, 2) = -0.9294999327444896e-1, (7, 3) = 0.6122617103835701e-1, (7, 4) = -0.4313615270778873e-1, (7, 5) = 0.4110148141424317e-1, (8, 1) = 0.6667910031326235e-1, (8, 2) = -0.5593040786446294e-1, (8, 3) = 0.42483062663230695e-1, (8, 4) = -0.2150725154063105e-1, (8, 5) = 0.21439202918624025e-1, (9, 1) = 0.3603568604801351e-1, (9, 2) = -0.3167753384430381e-1, (9, 3) = 0.26135864069716998e-1, (9, 4) = -0.10438939815596704e-1, (9, 5) = 0.10660108900785871e-1, (10, 1) = 0.18960327498140035e-1, (10, 2) = -0.1722319045196687e-1, (10, 3) = 0.14980312940540426e-1, (10, 4) = -0.4988937027048127e-2, (10, 5) = 0.5159686682556715e-2, (11, 1) = 0.9782165431635105e-2, (11, 2) = -0.910157017546314e-2, (11, 3) = 0.820665675837047e-2, (11, 4) = -0.2364269412330906e-2, (11, 5) = 0.24612927413180455e-2, (12, 1) = 0.49724019908313965e-2, (12, 2) = -0.47113528942048085e-2, (12, 3) = 0.4359613237292593e-2, (12, 4) = -0.11153042237558037e-2, (12, 5) = 0.11649711508526675e-2, (13, 1) = 0.24984995067600896e-2, (13, 2) = -0.2401250250975525e-2, (13, 3) = 0.22655973789531695e-2, (13, 4) = -0.5248289826886877e-3, (13, 5) = 0.549128934106459e-3, (14, 1) = 0.12440119569314578e-2, (14, 2) = -0.12093215573985628e-2, (14, 3) = 0.11583494838774682e-2, (14, 4) = -0.2466587850586314e-3, (14, 5) = 0.2582976297565444e-3, (15, 1) = 0.6148015308811455e-3, (15, 2) = -0.6032811800317005e-3, (15, 3) = 0.5848477187234688e-3, (15, 4) = -0.11584628661588081e-3, (15, 5) = 0.12136351684889346e-3, (16, 1) = 0.30197726796083954e-3, (16, 2) = -0.2986490288978108e-3, (16, 3) = 0.29237649937883e-3, (16, 4) = -0.5439103696428884e-4, (16, 5) = 0.56993214408891095e-4, (17, 1) = 0.14755307935715694e-3, (17, 2) = -0.14690575453443246e-3, (17, 3) = 0.14499494333704743e-3, (17, 4) = -0.25532771206319318e-4, (17, 5) = 0.2675702078834315e-4, (18, 1) = 0.7177236700295585e-4, (18, 2) = -0.7187729398053743e-4, (18, 3) = 0.7143005172186065e-4, (18, 4) = -0.11984713858579463e-4, (18, 5) = 0.1255997924657351e-4, (19, 1) = 0.3477022315080817e-4, (19, 2) = -0.35007749994105596e-4, (19, 3) = 0.3499403148041789e-4, (19, 4) = -0.5625174866621487e-5, (19, 5) = 0.589532422011194e-5, (20, 1) = 0.167801854213613e-4, (20, 2) = -0.16983543378325293e-4, (20, 3) = 0.17063175277423634e-4, (20, 4) = -0.2640190816045617e-5, (20, 5) = 0.27670182261114854e-5, (21, 1) = 0.8066191186382534e-5, (21, 2) = -0.821104246872564e-5, (21, 3) = 0.828660617992783e-5, (21, 4) = -0.12391870423047207e-5, (21, 5) = 0.12987213913763072e-5, (22, 1) = 0.3859180935593867e-5, (22, 2) = -0.395755789320176e-5, (22, 3) = 0.4010386715431575e-5, (22, 4) = -0.5816313926576407e-6, (22, 5) = 0.6095763839708823e-6, (23, 1) = 0.18341823395610769e-5, (23, 2) = -0.19019345748834397e-5, (23, 3) = 0.19350330892911135e-5, (23, 4) = -0.2730071797956253e-6, (23, 5) = 0.28612441556520465e-6, (24, 1) = 0.8623290091477282e-6, (24, 2) = -0.9113341483838946e-6, (24, 3) = 0.931230468673015e-6, (24, 4) = -0.1281526473802194e-6, (24, 5) = 0.1343101069871441e-6, (25, 1) = 0.39734387332399116e-6, (25, 2) = -0.4351065480638164e-6, (25, 3) = 0.44709019111609976e-6, (25, 4) = -0.6015514998812785e-7, (25, 5) = 0.6304549361391542e-7, (26, 1) = 0.17577216090080783e-6, (26, 2) = -0.2066547856380797e-6, (26, 3) = 0.21417714781972993e-6, (26, 4) = -0.2823339143989368e-7, (26, 5) = 0.29589957438210912e-7, (27, 1) = 0.7087967992164601e-7, (27, 2) = -0.9729618184580756e-7, (27, 3) = 0.10239949399678307e-6, (27, 4) = -0.13249689734274169e-7, (27, 5) = 0.13886315345671458e-7, (28, 1) = 0.2201947952838702e-7, (28, 2) = -0.45280562029436684e-7, (28, 3) = 0.4911313445931053e-7, (28, 4) = -0.6248707867260407e-8, (28, 5) = 0.6548948046607739e-8, (29, 1) = .0, (29, 2) = -0.20841183539706994e-7, (29, 3) = 0.24026825208835925e-7, (29, 4) = -0.30115916942592686e-8, (29, 5) = 0.31562937567380326e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.947670133699624e-8, (1, 4) = .0, (1, 5) = -0.16801628863722625e-8, (2, 1) = -0.5562688680729497e-9, (2, 2) = -0.21544394426163097e-8, (2, 3) = 0.287293894307546e-8, (2, 4) = -0.37357656722536194e-8, (2, 5) = 0.32217191547761024e-8, (3, 1) = -0.8350526558565278e-8, (3, 2) = 0.4134830634172977e-8, (3, 3) = 0.12491061704911204e-8, (3, 4) = 0.3909918765623829e-8, (3, 5) = -0.20757291059677243e-9, (4, 1) = 0.16671389719705844e-9, (4, 2) = 0.3648160715899586e-8, (4, 3) = -0.528396986802508e-8, (4, 4) = 0.4823828777432993e-9, (4, 5) = -0.2408743014606509e-8, (5, 1) = 0.5571634668634835e-8, (5, 2) = -0.5437715786747662e-8, (5, 3) = 0.33059473772110423e-8, (5, 4) = -0.32522595808460493e-8, (5, 5) = 0.24277913015859777e-8, (6, 1) = -0.25669375582958455e-9, (6, 2) = -0.24447686990555343e-8, (6, 3) = 0.37763491733330965e-8, (6, 4) = 0.16312740125029958e-9, (6, 5) = 0.2836817825937946e-9, (7, 1) = -0.32389377868904443e-8, (7, 2) = 0.1881042655673872e-8, (7, 3) = -0.11396650576233194e-8, (7, 4) = 0.10620111323548136e-8, (7, 5) = -0.9612930708926523e-9, (8, 1) = -0.18812922832728336e-8, (8, 2) = 0.14232046751044453e-8, (8, 3) = -0.1537803668361072e-8, (8, 4) = 0.1770842620028042e-9, (8, 5) = -0.15945787869057221e-9, (9, 1) = -0.4702411602328281e-9, (9, 2) = 0.320333402872091e-11, (9, 3) = -0.9185162120441862e-10, (9, 4) = -0.19095599932287843e-9, (9, 5) = 0.23643248136766287e-9, (10, 1) = -0.17417744006906416e-9, (10, 2) = -0.4092039771380655e-9, (10, 3) = 0.4774557415611376e-9, (10, 4) = -0.11595631798509842e-9, (10, 5) = 0.14655938678934742e-9, (11, 1) = -0.36430615951141193e-9, (11, 2) = -0.22503070324966588e-9, (11, 3) = 0.31318800713246974e-9, (11, 4) = -0.7102340842716831e-11, (11, 5) = 0.14634454169986603e-10, (12, 1) = -0.5396388972588783e-9, (12, 2) = -0.10024023632452876e-10, (12, 3) = 0.52585615313555275e-10, (12, 4) = 0.30763893139739825e-10, (12, 5) = -0.34005653195770876e-10, (13, 1) = -0.5943567114066009e-9, (13, 2) = 0.7448998028657788e-10, (13, 3) = -0.708034730465589e-10, (13, 4) = 0.26507725195353555e-10, (13, 5) = -0.3134708409282319e-10, (14, 1) = -0.5789647343263283e-9, (14, 2) = 0.6946997649814925e-10, (14, 3) = -0.8160855192822036e-10, (14, 4) = 0.12965812897819388e-10, (14, 5) = -0.16205118685268952e-10, (15, 1) = -0.5480288674538708e-9, (15, 2) = 0.3755086868784173e-10, (15, 3) = -0.50490114989597235e-10, (15, 4) = 0.32350773786510558e-11, (15, 5) = -0.4700861305885854e-11, (16, 1) = -0.5257284342112479e-9, (16, 2) = 0.10919861164588246e-10, (16, 3) = -0.19346772632557297e-10, (16, 4) = -0.11790344440137198e-11, (16, 5) = 0.832624535476741e-12, (17, 1) = -0.5155200016654919e-9, (17, 2) = -0.30465560714292855e-11, (17, 3) = -0.8267473293057957e-12, (17, 4) = -0.22320654114644123e-11, (17, 5) = 0.2400655612059856e-11, (18, 1) = -0.5133923272616294e-9, (18, 2) = -0.737945441660333e-11, (18, 3) = 0.64527937509837154e-11, (18, 4) = -0.18460323317176304e-11, (18, 5) = 0.21645324044442117e-11, (19, 1) = -0.5148896773711696e-9, (19, 2) = -0.6805942618791494e-11, (19, 3) = 0.7290389637347693e-11, (19, 4) = -0.1127780748270535e-11, (19, 5) = 0.1426574333434267e-11, (20, 1) = -0.5172260423041393e-9, (20, 2) = -0.4657799114489725e-11, (20, 3) = 0.5567830559435603e-11, (20, 4) = -0.5303365272165861e-12, (20, 5) = 0.7538287303084591e-12, (21, 1) = -0.5191746746088076e-9, (21, 2) = -0.25874975582162318e-11, (21, 3) = 0.3436128045689803e-11, (21, 4) = -0.15574116810816628e-12, (21, 5) = 0.30144441341623344e-12, (22, 1) = -0.5204375227141072e-9, (22, 2) = -0.11365161545683807e-11, (22, 3) = 0.1752985745214996e-11, (22, 4) = 0.3249627740759922e-13, (22, 5) = 0.5150782611193112e-13, (23, 1) = -0.5211213531601294e-9, (23, 2) = -0.3082774300480712e-12, (23, 3) = 0.6809547502858554e-12, (23, 4) = 0.10140915458196715e-12, (23, 5) = -0.6050324746005763e-13, (24, 1) = -0.5214281864248747e-9, (24, 2) = 0.7242912386800786e-13, (24, 3) = 0.10576899938353571e-12, (24, 4) = 0.1072206483365034e-12, (24, 5) = -0.9414790219756612e-13, (25, 1) = -0.5215366608792588e-9, (25, 2) = 0.1891469519098857e-12, (25, 3) = -0.14497650859163652e-12, (25, 4) = 0.8641875813257649e-13, (25, 5) = -0.9035857945464468e-13, (26, 1) = -0.5215615175319244e-9, (26, 2) = 0.17670718185401007e-12, (26, 3) = -0.2150167149653954e-12, (26, 4) = 0.5891552332814735e-13, (26, 5) = -0.7282784304094444e-13, (27, 1) = -0.5215650870134602e-9, (27, 2) = 0.11694313367520813e-12, (27, 3) = -0.20000655303758359e-12, (27, 4) = 0.3377761208360633e-13, (27, 5) = -0.53341189571616226e-13, (28, 1) = -0.521579349038632e-9, (28, 2) = 0.5209631819213893e-13, (28, 3) = -0.15467632068966293e-12, (28, 4) = 0.14064084565986249e-13, (28, 5) = -0.3672938482279342e-13, (29, 1) = -0.5216042456082603e-9, (29, 2) = .0, (29, 3) = -0.10651195375400426e-12, (29, 4) = .0, (29, 5) = -0.24309258949721638e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 29, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 29, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187987466566, (2) = 18446884187987467006, (3) = 18446884187987467270, (4) = 18446884187987467446, (5) = 18446884187987467622, (6) = 18446884187987467798}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else h := pointto(data[2][5]); return ('h')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc, D(h) = proc (y) local res, data, solnproc, `D(h)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .9220907462515571, (1, 4) = 1.0, (1, 5) = -.38783340466369254, (2, 1) = .16735567649115993, (2, 2) = .4202740870445161, (2, 3) = .3373570222677326, (2, 4) = .7355419804808778, (2, 5) = -.37712948659838486, (3, 1) = .503981373982817, (3, 2) = .5163794040551701, (3, 3) = -0.19185064713216023e-1, (3, 4) = .49172724293359593, (3, 5) = -.3229448930949884, (4, 1) = .8416523710936388, (4, 2) = .4417990492201716, (4, 3) = -.16651332416146195, (4, 4) = .2977138055168734, (4, 5) = -.23454549848673548, (5, 1) = 1.1062594162789947, (5, 2) = .31549674554502644, (5, 3) = -.18074641710244985, (5, 4) = .1656168899679353, (5, 5) = -.14708087178570156, (6, 1) = 1.2861729052641508, (6, 2) = .20118216105468362, (6, 3) = -.14047902635042844, (6, 4) = 0.8647526508575375e-1, (6, 5) = -0.8263424709324725e-1, (7, 1) = 1.3974860750621676, (7, 2) = .11890906506576693, (7, 3) = -0.9294999327444896e-1, (7, 4) = 0.4326575279767381e-1, (7, 5) = -0.4313615270778873e-1, (8, 1) = 1.462026155282785, (8, 2) = 0.6667910031326235e-1, (8, 3) = -0.5593040786446294e-1, (8, 4) = 0.21068777926171442e-1, (8, 5) = -0.2150725154063105e-1, (9, 1) = 1.497740830391555, (9, 2) = 0.3603568604801351e-1, (9, 3) = -0.3167753384430381e-1, (9, 4) = 0.10096973148301623e-1, (9, 5) = -0.10438939815596704e-1, (10, 1) = 1.516864299292917, (10, 2) = 0.18960327498140035e-1, (10, 3) = -0.1722319045196687e-1, (10, 4) = 0.4793366106261327e-2, (10, 5) = -0.4988937027048127e-2, (11, 1) = 1.5268547661160343, (11, 2) = 0.9782165431635105e-2, (11, 3) = -0.910157017546314e-2, (11, 4) = 0.22637704730545526e-2, (11, 5) = -0.2364269412330906e-2, (12, 1) = 1.5319805288911161, (12, 2) = 0.49724019908313965e-2, (12, 3) = -0.47113528942048085e-2, (12, 4) = 0.10660248274790495e-2, (12, 5) = -0.11153042237558037e-2, (13, 1) = 1.5345743659775581, (13, 2) = 0.24984995067600896e-2, (13, 3) = -0.2401250250975525e-2, (13, 4) = 0.5011966820226343e-3, (13, 5) = -0.5248289826886877e-3, (14, 1) = 1.5358728194208906, (14, 2) = 0.12440119569314578e-2, (14, 3) = -0.12093215573985628e-2, (14, 4) = 0.23544738145817105e-3, (14, 5) = -0.2466587850586314e-3, (15, 1) = 1.5365173102346918, (15, 2) = 0.6148015308811455e-3, (15, 3) = -0.6032811800317005e-3, (15, 4) = 0.11055525378085771e-3, (15, 5) = -0.11584628661588081e-3, (16, 1) = 1.536834972545, (16, 2) = 0.30197726796083954e-3, (16, 3) = -0.2986490288978108e-3, (16, 4) = 0.51899799851421e-4, (16, 5) = -0.5439103696428884e-4, (17, 1) = 1.5369906451774888, (17, 2) = 0.14755307935715694e-3, (17, 3) = -0.14690575453443246e-3, (17, 4) = 0.2436052045018883e-4, (17, 5) = -0.25532771206319318e-4, (18, 1) = 1.537066559314411, (18, 2) = 0.7177236700295585e-4, (18, 3) = -0.7187729398053743e-4, (18, 4) = 0.11432662628093271e-4, (18, 5) = -0.11984713858579463e-4, (19, 1) = 1.537103419510933, (19, 2) = 0.3477022315080817e-4, (19, 3) = -0.35007749994105596e-4, (19, 4) = 0.5364472172783753e-5, (19, 5) = -0.5625174866621487e-5, (20, 1) = 1.53712124655263, (20, 2) = 0.167801854213613e-4, (20, 3) = -0.16983543378325293e-4, (20, 4) = 0.2516289536316785e-5, (20, 5) = -0.2640190816045617e-5, (21, 1) = 1.5371298351182954, (21, 2) = 0.8066191186382534e-5, (21, 3) = -0.821104246872564e-5, (21, 4) = 0.11795051188684695e-5, (21, 5) = -0.12391870423047207e-5, (22, 1) = 1.537133955359844, (22, 2) = 0.3859180935593867e-5, (22, 3) = -0.395755789320176e-5, (22, 4) = 0.5520931946642665e-6, (22, 5) = -0.5816313926576407e-6, (23, 1) = 1.5371359212718083, (23, 2) = 0.18341823395610769e-5, (23, 3) = -0.19019345748834397e-5, (23, 4) = 0.2576175590429348e-6, (23, 5) = -0.2730071797956253e-6, (24, 1) = 1.5371368515706798, (24, 2) = 0.8623290091477282e-6, (24, 3) = -0.9113341483838946e-6, (24, 4) = 0.1194038808143948e-6, (24, 5) = -0.1281526473802194e-6, (25, 1) = 1.537137285591093, (25, 2) = 0.39734387332399116e-6, (25, 3) = -0.4351065480638164e-6, (25, 4) = 0.5452376150027097e-7, (25, 5) = -0.6015514998812785e-7, (26, 1) = 1.5371374825833801, (26, 2) = 0.17577216090080783e-6, (26, 3) = -0.2066547856380797e-6, (26, 4) = 0.24065480347840778e-7, (26, 5) = -0.2823339143989368e-7, (27, 1) = 1.5371375668997003, (27, 2) = 0.7087967992164601e-7, (27, 3) = -0.9729618184580756e-7, (27, 4) = 0.9768720688503002e-8, (27, 5) = -0.13249689734274169e-7, (28, 1) = 1.5371375980011175, (28, 2) = 0.2201947952838702e-7, (28, 3) = -0.45280562029436684e-7, (28, 4) = 0.30887065486698873e-8, (28, 5) = -0.6248707867260407e-8, (29, 1) = 1.537137604689266, (29, 2) = .0, (29, 3) = -0.20841183539706994e-7, (29, 4) = .0, (29, 5) = -0.30115916942592686e-8}, datatype = float[8], order = C_order); YP := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .9220907462515571, (1, 3) = -1.0, (1, 4) = -.38783340466369254, (1, 5) = .0, (2, 1) = .4202740870445161, (2, 2) = .3373570222677326, (2, 3) = -.6895707858708219, (2, 4) = -.37712948659838486, (2, 5) = 0.4303279115075219e-1, (3, 1) = .5163794040551701, (3, 2) = -0.19185064713216023e-1, (3, 3) = -.3511517120118227, (3, 4) = -.3229448930949884, (3, 5) = .11097150746096335, (4, 1) = .4417990492201716, (4, 2) = -.16651332416146195, (4, 3) = -0.9501085499656597e-1, (4, 4) = -.23454549848673548, (4, 5) = .13459484654365939, (5, 1) = .31549674554502644, (5, 2) = -.18074641710244985, (5, 3) = 0.3411652766552317e-1, (5, 4) = -.14708087178570156, (5, 5) = .11093836320508359, (6, 1) = .20118216105468362, (6, 2) = -.14047902635042844, (6, 3) = 0.6927210396491991e-1, (6, 4) = -0.8263424709324725e-1, (6, 5) = 0.7246495203970743e-1, (7, 1) = .11890906506576693, (7, 2) = -0.9294999327444896e-1, (7, 3) = 0.6122617103835701e-1, (7, 4) = -0.4313615270778873e-1, (7, 5) = 0.4110148141424317e-1, (8, 1) = 0.6667910031326235e-1, (8, 2) = -0.5593040786446294e-1, (8, 3) = 0.42483062663230695e-1, (8, 4) = -0.2150725154063105e-1, (8, 5) = 0.21439202918624025e-1, (9, 1) = 0.3603568604801351e-1, (9, 2) = -0.3167753384430381e-1, (9, 3) = 0.26135864069716998e-1, (9, 4) = -0.10438939815596704e-1, (9, 5) = 0.10660108900785871e-1, (10, 1) = 0.18960327498140035e-1, (10, 2) = -0.1722319045196687e-1, (10, 3) = 0.14980312940540426e-1, (10, 4) = -0.4988937027048127e-2, (10, 5) = 0.5159686682556715e-2, (11, 1) = 0.9782165431635105e-2, (11, 2) = -0.910157017546314e-2, (11, 3) = 0.820665675837047e-2, (11, 4) = -0.2364269412330906e-2, (11, 5) = 0.24612927413180455e-2, (12, 1) = 0.49724019908313965e-2, (12, 2) = -0.47113528942048085e-2, (12, 3) = 0.4359613237292593e-2, (12, 4) = -0.11153042237558037e-2, (12, 5) = 0.11649711508526675e-2, (13, 1) = 0.24984995067600896e-2, (13, 2) = -0.2401250250975525e-2, (13, 3) = 0.22655973789531695e-2, (13, 4) = -0.5248289826886877e-3, (13, 5) = 0.549128934106459e-3, (14, 1) = 0.12440119569314578e-2, (14, 2) = -0.12093215573985628e-2, (14, 3) = 0.11583494838774682e-2, (14, 4) = -0.2466587850586314e-3, (14, 5) = 0.2582976297565444e-3, (15, 1) = 0.6148015308811455e-3, (15, 2) = -0.6032811800317005e-3, (15, 3) = 0.5848477187234688e-3, (15, 4) = -0.11584628661588081e-3, (15, 5) = 0.12136351684889346e-3, (16, 1) = 0.30197726796083954e-3, (16, 2) = -0.2986490288978108e-3, (16, 3) = 0.29237649937883e-3, (16, 4) = -0.5439103696428884e-4, (16, 5) = 0.56993214408891095e-4, (17, 1) = 0.14755307935715694e-3, (17, 2) = -0.14690575453443246e-3, (17, 3) = 0.14499494333704743e-3, (17, 4) = -0.25532771206319318e-4, (17, 5) = 0.2675702078834315e-4, (18, 1) = 0.7177236700295585e-4, (18, 2) = -0.7187729398053743e-4, (18, 3) = 0.7143005172186065e-4, (18, 4) = -0.11984713858579463e-4, (18, 5) = 0.1255997924657351e-4, (19, 1) = 0.3477022315080817e-4, (19, 2) = -0.35007749994105596e-4, (19, 3) = 0.3499403148041789e-4, (19, 4) = -0.5625174866621487e-5, (19, 5) = 0.589532422011194e-5, (20, 1) = 0.167801854213613e-4, (20, 2) = -0.16983543378325293e-4, (20, 3) = 0.17063175277423634e-4, (20, 4) = -0.2640190816045617e-5, (20, 5) = 0.27670182261114854e-5, (21, 1) = 0.8066191186382534e-5, (21, 2) = -0.821104246872564e-5, (21, 3) = 0.828660617992783e-5, (21, 4) = -0.12391870423047207e-5, (21, 5) = 0.12987213913763072e-5, (22, 1) = 0.3859180935593867e-5, (22, 2) = -0.395755789320176e-5, (22, 3) = 0.4010386715431575e-5, (22, 4) = -0.5816313926576407e-6, (22, 5) = 0.6095763839708823e-6, (23, 1) = 0.18341823395610769e-5, (23, 2) = -0.19019345748834397e-5, (23, 3) = 0.19350330892911135e-5, (23, 4) = -0.2730071797956253e-6, (23, 5) = 0.28612441556520465e-6, (24, 1) = 0.8623290091477282e-6, (24, 2) = -0.9113341483838946e-6, (24, 3) = 0.931230468673015e-6, (24, 4) = -0.1281526473802194e-6, (24, 5) = 0.1343101069871441e-6, (25, 1) = 0.39734387332399116e-6, (25, 2) = -0.4351065480638164e-6, (25, 3) = 0.44709019111609976e-6, (25, 4) = -0.6015514998812785e-7, (25, 5) = 0.6304549361391542e-7, (26, 1) = 0.17577216090080783e-6, (26, 2) = -0.2066547856380797e-6, (26, 3) = 0.21417714781972993e-6, (26, 4) = -0.2823339143989368e-7, (26, 5) = 0.29589957438210912e-7, (27, 1) = 0.7087967992164601e-7, (27, 2) = -0.9729618184580756e-7, (27, 3) = 0.10239949399678307e-6, (27, 4) = -0.13249689734274169e-7, (27, 5) = 0.13886315345671458e-7, (28, 1) = 0.2201947952838702e-7, (28, 2) = -0.45280562029436684e-7, (28, 3) = 0.4911313445931053e-7, (28, 4) = -0.6248707867260407e-8, (28, 5) = 0.6548948046607739e-8, (29, 1) = .0, (29, 2) = -0.20841183539706994e-7, (29, 3) = 0.24026825208835925e-7, (29, 4) = -0.30115916942592686e-8, (29, 5) = 0.31562937567380326e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(29, {(1) = .0, (2) = .6868475688873201, (3) = 1.3755694818864481, (4) = 2.0682143718350936, (5) = 2.7656618600289473, (6) = 3.4686284253590123, (7) = 4.17661098003989, (8) = 4.889009254798094, (9) = 5.6045212988808935, (10) = 6.3224529780942005, (11) = 7.0418659844902995, (12) = 7.762245674819311, (13) = 8.483238223424435, (14) = 9.204551333871233, (15) = 9.926070501029098, (16) = 10.64768103013191, (17) = 11.369348833520784, (18) = 12.091054342052754, (19) = 12.812781373230616, (20) = 13.534515985945216, (21) = 14.256239622887145, (22) = 14.977939582148815, (23) = 15.699604511035915, (24) = 16.4212086528194, (25) = 17.14283044113223, (26) = 17.864572619901118, (27) = 18.58641890913639, (28) = 19.30355908510746, (29) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(29, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.947670133699624e-8, (1, 4) = .0, (1, 5) = -0.16801628863722625e-8, (2, 1) = -0.5562688680729497e-9, (2, 2) = -0.21544394426163097e-8, (2, 3) = 0.287293894307546e-8, (2, 4) = -0.37357656722536194e-8, (2, 5) = 0.32217191547761024e-8, (3, 1) = -0.8350526558565278e-8, (3, 2) = 0.4134830634172977e-8, (3, 3) = 0.12491061704911204e-8, (3, 4) = 0.3909918765623829e-8, (3, 5) = -0.20757291059677243e-9, (4, 1) = 0.16671389719705844e-9, (4, 2) = 0.3648160715899586e-8, (4, 3) = -0.528396986802508e-8, (4, 4) = 0.4823828777432993e-9, (4, 5) = -0.2408743014606509e-8, (5, 1) = 0.5571634668634835e-8, (5, 2) = -0.5437715786747662e-8, (5, 3) = 0.33059473772110423e-8, (5, 4) = -0.32522595808460493e-8, (5, 5) = 0.24277913015859777e-8, (6, 1) = -0.25669375582958455e-9, (6, 2) = -0.24447686990555343e-8, (6, 3) = 0.37763491733330965e-8, (6, 4) = 0.16312740125029958e-9, (6, 5) = 0.2836817825937946e-9, (7, 1) = -0.32389377868904443e-8, (7, 2) = 0.1881042655673872e-8, (7, 3) = -0.11396650576233194e-8, (7, 4) = 0.10620111323548136e-8, (7, 5) = -0.9612930708926523e-9, (8, 1) = -0.18812922832728336e-8, (8, 2) = 0.14232046751044453e-8, (8, 3) = -0.1537803668361072e-8, (8, 4) = 0.1770842620028042e-9, (8, 5) = -0.15945787869057221e-9, (9, 1) = -0.4702411602328281e-9, (9, 2) = 0.320333402872091e-11, (9, 3) = -0.9185162120441862e-10, (9, 4) = -0.19095599932287843e-9, (9, 5) = 0.23643248136766287e-9, (10, 1) = -0.17417744006906416e-9, (10, 2) = -0.4092039771380655e-9, (10, 3) = 0.4774557415611376e-9, (10, 4) = -0.11595631798509842e-9, (10, 5) = 0.14655938678934742e-9, (11, 1) = -0.36430615951141193e-9, (11, 2) = -0.22503070324966588e-9, (11, 3) = 0.31318800713246974e-9, (11, 4) = -0.7102340842716831e-11, (11, 5) = 0.14634454169986603e-10, (12, 1) = -0.5396388972588783e-9, (12, 2) = -0.10024023632452876e-10, (12, 3) = 0.52585615313555275e-10, (12, 4) = 0.30763893139739825e-10, (12, 5) = -0.34005653195770876e-10, (13, 1) = -0.5943567114066009e-9, (13, 2) = 0.7448998028657788e-10, (13, 3) = -0.708034730465589e-10, (13, 4) = 0.26507725195353555e-10, (13, 5) = -0.3134708409282319e-10, (14, 1) = -0.5789647343263283e-9, (14, 2) = 0.6946997649814925e-10, (14, 3) = -0.8160855192822036e-10, (14, 4) = 0.12965812897819388e-10, (14, 5) = -0.16205118685268952e-10, (15, 1) = -0.5480288674538708e-9, (15, 2) = 0.3755086868784173e-10, (15, 3) = -0.50490114989597235e-10, (15, 4) = 0.32350773786510558e-11, (15, 5) = -0.4700861305885854e-11, (16, 1) = -0.5257284342112479e-9, (16, 2) = 0.10919861164588246e-10, (16, 3) = -0.19346772632557297e-10, (16, 4) = -0.11790344440137198e-11, (16, 5) = 0.832624535476741e-12, (17, 1) = -0.5155200016654919e-9, (17, 2) = -0.30465560714292855e-11, (17, 3) = -0.8267473293057957e-12, (17, 4) = -0.22320654114644123e-11, (17, 5) = 0.2400655612059856e-11, (18, 1) = -0.5133923272616294e-9, (18, 2) = -0.737945441660333e-11, (18, 3) = 0.64527937509837154e-11, (18, 4) = -0.18460323317176304e-11, (18, 5) = 0.21645324044442117e-11, (19, 1) = -0.5148896773711696e-9, (19, 2) = -0.6805942618791494e-11, (19, 3) = 0.7290389637347693e-11, (19, 4) = -0.1127780748270535e-11, (19, 5) = 0.1426574333434267e-11, (20, 1) = -0.5172260423041393e-9, (20, 2) = -0.4657799114489725e-11, (20, 3) = 0.5567830559435603e-11, (20, 4) = -0.5303365272165861e-12, (20, 5) = 0.7538287303084591e-12, (21, 1) = -0.5191746746088076e-9, (21, 2) = -0.25874975582162318e-11, (21, 3) = 0.3436128045689803e-11, (21, 4) = -0.15574116810816628e-12, (21, 5) = 0.30144441341623344e-12, (22, 1) = -0.5204375227141072e-9, (22, 2) = -0.11365161545683807e-11, (22, 3) = 0.1752985745214996e-11, (22, 4) = 0.3249627740759922e-13, (22, 5) = 0.5150782611193112e-13, (23, 1) = -0.5211213531601294e-9, (23, 2) = -0.3082774300480712e-12, (23, 3) = 0.6809547502858554e-12, (23, 4) = 0.10140915458196715e-12, (23, 5) = -0.6050324746005763e-13, (24, 1) = -0.5214281864248747e-9, (24, 2) = 0.7242912386800786e-13, (24, 3) = 0.10576899938353571e-12, (24, 4) = 0.1072206483365034e-12, (24, 5) = -0.9414790219756612e-13, (25, 1) = -0.5215366608792588e-9, (25, 2) = 0.1891469519098857e-12, (25, 3) = -0.14497650859163652e-12, (25, 4) = 0.8641875813257649e-13, (25, 5) = -0.9035857945464468e-13, (26, 1) = -0.5215615175319244e-9, (26, 2) = 0.17670718185401007e-12, (26, 3) = -0.2150167149653954e-12, (26, 4) = 0.5891552332814735e-13, (26, 5) = -0.7282784304094444e-13, (27, 1) = -0.5215650870134602e-9, (27, 2) = 0.11694313367520813e-12, (27, 3) = -0.20000655303758359e-12, (27, 4) = 0.3377761208360633e-13, (27, 5) = -0.53341189571616226e-13, (28, 1) = -0.521579349038632e-9, (28, 2) = 0.5209631819213893e-13, (28, 3) = -0.15467632068966293e-12, (28, 4) = 0.14064084565986249e-13, (28, 5) = -0.3672938482279342e-13, (29, 1) = -0.5216042456082603e-9, (29, 2) = .0, (29, 3) = -0.10651195375400426e-12, (29, 4) = .0, (29, 5) = -0.24309258949721638e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 29, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(29, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[29] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(9.47670133699624e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 29, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[29] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[29] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(29, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187987466566, (2) = 18446884187987467006, (3) = 18446884187987467270, (4) = 18446884187987467446, (5) = 18446884187987467622, (6) = 18446884187987467798}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `D(h)` := pointto(data[2][6]); return ('`D(h)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc]

sol2 := dsolve([eval(sys_ode, n = 1), ics], numeric, output = operator, continuation = lambda)

[y = proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .7509958992140092, (1, 4) = 1.0, (1, 5) = -.5766182177889736, (2, 1) = .19294506823253071, (2, 2) = .345717339320025, (2, 3) = .11748530886258848, (2, 4) = .5437094913262883, (2, 5) = -.42619398711861173, (3, 1) = .5054078147971317, (3, 2) = .3295368928873986, (3, 3) = -.10281256306809654, (3, 4) = .25842450171487663, (3, 5) = -.22929557876687195, (4, 1) = .7517816685489124, (4, 2) = .2211740580910692, (4, 3) = -.12239573074044155, (4, 4) = .11436339993638699, (4, 5) = -.10715356554772232, (5, 1) = .9054483747328635, (5, 2) = .1264140268653532, (5, 3) = -0.8591949919337281e-1, (5, 4) = 0.48719039228723914e-1, (5, 5) = -0.4672290447819592e-1, (6, 1) = .9900111442791364, (6, 2) = 0.6583176447988233e-1, (6, 3) = -0.4973034058218495e-1, (6, 4) = 0.20344942782691302e-1, (6, 5) = -0.1969778835995821e-1, (7, 1) = 1.0330480370810036, (7, 2) = 0.32315267535371534e-1, (7, 3) = -0.2600272586003493e-1, (7, 4) = 0.841131598460929e-2, (7, 5) = -0.8174310046940966e-2, (8, 1) = 1.0538493557885784, (8, 2) = 0.15247583407686798e-1, (8, 3) = -0.12786769213836738e-1, (8, 4) = 0.3460729946239088e-2, (8, 5) = -0.3368066407962972e-2, (9, 1) = 1.0635555317661158, (9, 2) = 0.6998105041282296e-2, (9, 3) = -0.604035420324911e-2, (9, 4) = 0.14206067753971528e-2, (9, 5) = -0.13833280384499146e-2, (10, 1) = 1.067973284021565, (10, 2) = 0.31478225677167735e-2, (10, 3) = -0.2774978205981712e-2, (10, 4) = 0.582512305832151e-3, (10, 5) = -0.5673463700191876e-3, (11, 1) = 1.0699476410036053, (11, 2) = 0.13945650673762352e-2, (11, 3) = -0.12492766558546968e-2, (11, 4) = 0.23873182831542274e-3, (11, 5) = -0.23253747538797784e-3, (12, 1) = 1.070817852106119, (12, 2) = 0.6105700389362067e-3, (12, 3) = -0.553893319523471e-3, (12, 4) = 0.9781649764191596e-4, (12, 5) = -0.9528435644133216e-4, (13, 1) = 1.071197262363775, (13, 2) = 0.26480452107368317e-3, (13, 3) = -0.24268469519682714e-3, (13, 4) = 0.4007386033544328e-4, (13, 5) = -0.39040038537364915e-4, (14, 1) = 1.0713612440610472, (14, 2) = 0.11394909512081752e-3, (14, 3) = -0.10532867430154103e-3, (14, 4) = 0.16415288070247586e-4, (14, 5) = -0.15995006093854115e-4, (15, 1) = 1.0714315982101714, (15, 2) = 0.4870000930855666e-4, (15, 3) = -0.45361559105776056e-4, (15, 4) = 0.6722049068016235e-5, (15, 5) = -0.655308793716169e-5, (16, 1) = 1.071461583562454, (16, 2) = 0.20679444144369147e-4, (16, 3) = -0.1941000219193855e-4, (16, 4) = 0.2750733132001786e-5, (16, 5) = -0.26847296756546684e-5, (17, 1) = 1.0714742787121994, (17, 2) = 0.8718850547396554e-5, (17, 3) = -0.8259728398401262e-5, (17, 4) = 0.11237385463905423e-5, (17, 5) = -0.10999141617991744e-5, (18, 1) = 1.0714796105551125, (18, 2) = 0.3640252978905283e-5, (18, 3) = -0.3497402269851553e-5, (18, 4) = 0.45718005927355556e-6, (18, 5) = -0.45063567228372506e-6, (19, 1) = 1.0714818225105625, (19, 2) = 0.14944389063713663e-5, (19, 3) = -0.14735566530371413e-5, (19, 4) = 0.18409802069572952e-6, (19, 5) = -0.1846330205946365e-6, (20, 1) = 1.0714827192138023, (20, 2) = 0.5925773918561377e-6, (20, 3) = -0.6170979188394264e-6, (20, 4) = 0.7221359286521267e-7, (20, 5) = -0.756490724910656e-7, (21, 1) = 1.071483064754158, (21, 2) = 0.2162423610813038e-6, (21, 3) = -0.25593520469778174e-6, (21, 4) = 0.26367855391509727e-7, (21, 5) = -0.3099182802156362e-7, (22, 1) = 1.07148318136988, (22, 2) = 0.6124869999887661e-7, (22, 3) = -0.10415162185182523e-6, (22, 4) = 0.7586701144665916e-8, (22, 5) = -0.12697548109268844e-7, (23, 1) = 1.0714832046525464, (23, 2) = .0, (23, 3) = -0.414339042389871e-7, (23, 4) = .0, (23, 5) = -0.5307519484383215e-8}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .7509958992140092, (1, 3) = -1.0, (1, 4) = -.5766182177889736, (1, 5) = .0, (2, 1) = .345717339320025, (2, 2) = .11748530886258848, (2, 3) = -.44685722355458307, (2, 4) = -.42619398711861173, (2, 5) = .2456380242084213, (3, 1) = .3295368928873986, (3, 2) = -.10281256306809654, (3, 3) = -0.9786766510705683e-1, (3, 4) = -.22929557876687195, (3, 5) = .1827710770439118, (4, 1) = .2211740580910692, (4, 2) = -.12239573074044155, (4, 3) = 0.26569430715397205e-1, (4, 4) = -.10715356554772232, (4, 5) = 0.9622754869041322e-1, (5, 1) = .1264140268653532, (5, 2) = -0.8591949919337281e-1, (5, 3) = 0.4505713786209132e-1, (5, 4) = -0.4672290447819592e-1, (5, 5) = 0.44058134414995835e-1, (6, 1) = 0.6583176447988233e-1, (6, 2) = -0.4973034058218495e-1, (6, 3) = 0.332224698170035e-1, (6, 4) = -0.1969778835995821e-1, (6, 5) = 0.18945794068761176e-1, (7, 1) = 0.32315267535371534e-1, (7, 2) = -0.2600272586003493e-1, (7, 3) = 0.19495025439737884e-1, (7, 4) = -0.8174310046940966e-2, (7, 5) = 0.792388079531917e-2, (8, 1) = 0.15247583407686798e-1, (8, 2) = -0.12786769213836738e-1, (8, 3) = 0.10247087352154351e-1, (8, 4) = -0.3368066407962972e-2, (8, 5) = 0.3274729438901535e-2, (9, 1) = 0.6998105041282296e-2, (9, 2) = -0.604035420324911e-2, (9, 3) = 0.5052618825463968e-2, (9, 4) = -0.13833280384499146e-2, (9, 5) = 0.13465343117974211e-2, (10, 1) = 0.31478225677167735e-2, (10, 2) = -0.2774978205981712e-2, (10, 3) = 0.2390999068816236e-2, (10, 4) = -0.5673463700191876e-3, (10, 5) = 0.5524949194085244e-3, (11, 1) = 0.13945650673762352e-2, (11, 2) = -0.12492766558546968e-2, (11, 3) = 0.1099873594304329e-2, (11, 4) = -0.23253747538797784e-3, (11, 5) = 0.22648713664049123e-3, (12, 1) = 0.6105700389362067e-3, (12, 2) = -0.553893319523471e-3, (12, 3) = 0.495675152838582e-3, (12, 4) = -0.9528435644133216e-4, (12, 5) = 0.9281083066054085e-4, (13, 1) = 0.26480452107368317e-3, (13, 2) = -0.24268469519682714e-3, (13, 3) = 0.21995944221136622e-3, (13, 4) = -0.39040038537364915e-4, (13, 5) = 0.3802744922108661e-4, (14, 1) = 0.11394909512081752e-3, (14, 2) = -0.10532867430154103e-3, (14, 3) = 0.9644275586103112e-4, (14, 4) = -0.15995006093854115e-4, (14, 5) = 0.15580272849724842e-4, (15, 1) = 0.4870000930855666e-4, (15, 2) = -0.45361559105776056e-4, (15, 3) = 0.41882130392897214e-4, (15, 4) = -0.655308793716169e-5, (15, 5) = 0.6383193495979208e-5, (16, 1) = 0.20679444144369147e-4, (16, 2) = -0.1941000219193855e-4, (16, 3) = 0.18046766192933517e-4, (16, 4) = -0.26847296756546684e-5, (16, 5) = 0.26151287212238395e-5, (17, 1) = 0.8718850547396554e-5, (17, 2) = -0.8259728398401262e-5, (17, 3) = 0.7726423999999988e-5, (17, 4) = -0.10999141617991744e-5, (17, 5) = 0.1071399573515949e-5, (18, 1) = 0.3640252978905283e-5, (18, 2) = -0.3497402269851553e-5, (18, 3) = 0.32902284142233035e-5, (18, 4) = -0.45063567228372506e-6, (18, 5) = 0.43895327171989055e-6, (19, 1) = 0.14944389063713663e-5, (19, 2) = -0.14735566530371413e-5, (19, 3) = 0.13947933808207162e-5, (19, 4) = -0.1846330205946365e-6, (19, 5) = 0.1798465459323782e-6, (20, 1) = 0.5925773918561377e-6, (20, 2) = -0.6170979188394264e-6, (20, 3) = 0.5889965143819995e-6, (20, 4) = -0.756490724910656e-7, (20, 5) = 0.7368792426442866e-7, (21, 1) = 0.2162423610813038e-6, (21, 2) = -0.25593520469778174e-6, (21, 3) = 0.24786242887731095e-6, (21, 4) = -0.3099182802156362e-7, (21, 5) = 0.3018838597520553e-7, (22, 1) = 0.6124869999887661e-7, (22, 2) = -0.10415162185182523e-6, (22, 3) = 0.10401001373336376e-6, (22, 4) = -0.12697548109268844e-7, (22, 5) = 0.12368372462174604e-7, (23, 1) = .0, (23, 2) = -0.414339042389871e-7, (23, 3) = 0.4439573249525663e-7, (23, 4) = -0.5307519484383215e-8, (23, 5) = 0.5169925441711597e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.18677723346185155e-6, (1, 4) = .0, (1, 5) = -0.1601034189830942e-6, (2, 1) = 0.37448226506023734e-7, (2, 2) = -0.4882419193663561e-8, (2, 3) = 0.32590922758163096e-7, (2, 4) = 0.8384642286135039e-8, (2, 5) = -0.3822989163192259e-7, (3, 1) = 0.4178076522983118e-7, (3, 2) = -0.32454728940560626e-7, (3, 3) = 0.5559818911848743e-7, (3, 4) = 0.255368475385125e-7, (3, 5) = -0.26372934101735208e-7, (4, 1) = -0.3503349256133378e-8, (4, 2) = 0.23271413239470415e-7, (4, 3) = -0.13109277388977377e-7, (4, 4) = 0.1940395871477904e-7, (4, 5) = -0.21150015818914884e-7, (5, 1) = 0.9049822894255894e-8, (5, 2) = 0.2044098278596014e-7, (5, 3) = -0.23457165838090578e-7, (5, 4) = 0.2721022646410278e-8, (5, 5) = -0.3786091636826618e-8, (6, 1) = 0.27051273759362853e-7, (6, 2) = 0.15343716259627215e-9, (6, 3) = -0.21958032487259045e-8, (6, 4) = -0.4159511453386257e-9, (6, 5) = 0.38101170586747216e-10, (7, 1) = 0.29235514018364573e-7, (7, 2) = -0.453106337656716e-8, (7, 3) = 0.46319249349793395e-8, (7, 4) = 0.46342814231151797e-9, (7, 5) = -0.6792806203548744e-9, (8, 1) = 0.26054556255110013e-7, (8, 2) = -0.1882133375224601e-8, (8, 3) = 0.2244789452496081e-8, (8, 4) = 0.711835820669783e-9, (8, 5) = -0.8568477954792043e-9, (9, 1) = 0.24106962716022037e-7, (9, 2) = 0.1629685214904445e-9, (9, 3) = -0.11146494499834733e-9, (9, 4) = 0.45110688737061194e-9, (9, 5) = -0.539236754168219e-9, (10, 1) = 0.2374177391716608e-7, (10, 2) = 0.5860236135721297e-9, (10, 3) = -0.7196114662102999e-9, (10, 4) = 0.18313053413689276e-9, (10, 5) = -0.23112721605478909e-9, (11, 1) = 0.23938814887888642e-7, (11, 2) = 0.34670384490097316e-9, (11, 3) = -0.499387007098935e-9, (11, 4) = 0.40264060755003194e-10, (11, 5) = -0.6396528893681144e-10, (12, 1) = 0.2413280997412847e-7, (12, 2) = 0.8123434213412095e-10, (12, 3) = -0.18766851557521373e-9, (12, 4) = -0.10028889791867737e-10, (12, 5) = -0.5607571181840299e-12, (13, 1) = 0.24205166580449604e-7, (13, 2) = -0.4873554507228097e-10, (13, 3) = -0.9122645013749574e-11, (13, 4) = -0.1774384229814944e-10, (13, 5) = 0.13554216810388484e-10, (14, 1) = 0.24197923253315855e-7, (14, 2) = -0.7644103795235015e-10, (14, 3) = 0.5059366630228127e-10, (14, 4) = -0.12500071087031085e-10, (14, 5) = 0.11123935740845305e-10, (15, 1) = 0.24164459411748233e-7, (15, 2) = -0.6066740320325875e-10, (15, 3) = 0.5144731921398412e-10, (15, 4) = -0.63139041944452e-11, (15, 5) = 0.6018851574113935e-11, (16, 1) = 0.24133003199149926e-7, (16, 2) = -0.36959226456229056e-10, (16, 3) = 0.34807094444056334e-10, (16, 4) = -0.2296584459403134e-11, (16, 5) = 0.2328976704823776e-11, (17, 1) = 0.24111780059612412e-7, (17, 2) = -0.1873228504203057e-10, (17, 3) = 0.18878272014729034e-10, (17, 4) = -0.33241174545583766e-12, (17, 5) = 0.40568885552430346e-12, (18, 1) = 0.24099883385166445e-7, (18, 2) = -0.7930627600316472e-11, (18, 3) = 0.8419004595137473e-11, (18, 4) = 0.3767477185747604e-12, (18, 5) = -0.34832143812623605e-12, (19, 1) = 0.2409407001294113e-7, (19, 2) = -0.26201105239283355e-11, (19, 3) = 0.2849865664815142e-11, (19, 4) = 0.485146485573298e-12, (19, 5) = -0.5118521121703797e-12, (20, 1) = 0.24091528694372805e-7, (20, 2) = -0.4820658103323563e-12, (20, 3) = 0.3930534221642779e-12, (20, 4) = 0.37341039360175125e-12, (20, 5) = -0.4432984456493013e-12, (21, 1) = 0.24090485353105713e-7, (21, 2) = 0.12932248130697764e-12, (21, 3) = -0.4349598146471398e-12, (21, 4) = 0.22003866786553054e-12, (21, 5) = -0.31866839336921104e-12, (22, 1) = 0.24090016159892753e-7, (22, 2) = 0.14345040328921917e-12, (22, 3) = -0.5483809312163577e-12, (22, 4) = 0.9076616249531766e-13, (22, 5) = -0.20691039898422648e-12, (23, 1) = 0.24089729356345837e-7, (23, 2) = .0, (23, 3) = -0.4163274954165759e-12, (23, 4) = .0, (23, 5) = -0.12614313243075443e-12}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187980970662, (2) = 18446884187980970838, (3) = 18446884187980971014, (4) = 18446884187980971190, (5) = 18446884187980971366, (6) = 18446884187980971542}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc, g = proc (y) local res, data, solnproc, g, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .7509958992140092, (1, 4) = 1.0, (1, 5) = -.5766182177889736, (2, 1) = .19294506823253071, (2, 2) = .345717339320025, (2, 3) = .11748530886258848, (2, 4) = .5437094913262883, (2, 5) = -.42619398711861173, (3, 1) = .5054078147971317, (3, 2) = .3295368928873986, (3, 3) = -.10281256306809654, (3, 4) = .25842450171487663, (3, 5) = -.22929557876687195, (4, 1) = .7517816685489124, (4, 2) = .2211740580910692, (4, 3) = -.12239573074044155, (4, 4) = .11436339993638699, (4, 5) = -.10715356554772232, (5, 1) = .9054483747328635, (5, 2) = .1264140268653532, (5, 3) = -0.8591949919337281e-1, (5, 4) = 0.48719039228723914e-1, (5, 5) = -0.4672290447819592e-1, (6, 1) = .9900111442791364, (6, 2) = 0.6583176447988233e-1, (6, 3) = -0.4973034058218495e-1, (6, 4) = 0.20344942782691302e-1, (6, 5) = -0.1969778835995821e-1, (7, 1) = 1.0330480370810036, (7, 2) = 0.32315267535371534e-1, (7, 3) = -0.2600272586003493e-1, (7, 4) = 0.841131598460929e-2, (7, 5) = -0.8174310046940966e-2, (8, 1) = 1.0538493557885784, (8, 2) = 0.15247583407686798e-1, (8, 3) = -0.12786769213836738e-1, (8, 4) = 0.3460729946239088e-2, (8, 5) = -0.3368066407962972e-2, (9, 1) = 1.0635555317661158, (9, 2) = 0.6998105041282296e-2, (9, 3) = -0.604035420324911e-2, (9, 4) = 0.14206067753971528e-2, (9, 5) = -0.13833280384499146e-2, (10, 1) = 1.067973284021565, (10, 2) = 0.31478225677167735e-2, (10, 3) = -0.2774978205981712e-2, (10, 4) = 0.582512305832151e-3, (10, 5) = -0.5673463700191876e-3, (11, 1) = 1.0699476410036053, (11, 2) = 0.13945650673762352e-2, (11, 3) = -0.12492766558546968e-2, (11, 4) = 0.23873182831542274e-3, (11, 5) = -0.23253747538797784e-3, (12, 1) = 1.070817852106119, (12, 2) = 0.6105700389362067e-3, (12, 3) = -0.553893319523471e-3, (12, 4) = 0.9781649764191596e-4, (12, 5) = -0.9528435644133216e-4, (13, 1) = 1.071197262363775, (13, 2) = 0.26480452107368317e-3, (13, 3) = -0.24268469519682714e-3, (13, 4) = 0.4007386033544328e-4, (13, 5) = -0.39040038537364915e-4, (14, 1) = 1.0713612440610472, (14, 2) = 0.11394909512081752e-3, (14, 3) = -0.10532867430154103e-3, (14, 4) = 0.16415288070247586e-4, (14, 5) = -0.15995006093854115e-4, (15, 1) = 1.0714315982101714, (15, 2) = 0.4870000930855666e-4, (15, 3) = -0.45361559105776056e-4, (15, 4) = 0.6722049068016235e-5, (15, 5) = -0.655308793716169e-5, (16, 1) = 1.071461583562454, (16, 2) = 0.20679444144369147e-4, (16, 3) = -0.1941000219193855e-4, (16, 4) = 0.2750733132001786e-5, (16, 5) = -0.26847296756546684e-5, (17, 1) = 1.0714742787121994, (17, 2) = 0.8718850547396554e-5, (17, 3) = -0.8259728398401262e-5, (17, 4) = 0.11237385463905423e-5, (17, 5) = -0.10999141617991744e-5, (18, 1) = 1.0714796105551125, (18, 2) = 0.3640252978905283e-5, (18, 3) = -0.3497402269851553e-5, (18, 4) = 0.45718005927355556e-6, (18, 5) = -0.45063567228372506e-6, (19, 1) = 1.0714818225105625, (19, 2) = 0.14944389063713663e-5, (19, 3) = -0.14735566530371413e-5, (19, 4) = 0.18409802069572952e-6, (19, 5) = -0.1846330205946365e-6, (20, 1) = 1.0714827192138023, (20, 2) = 0.5925773918561377e-6, (20, 3) = -0.6170979188394264e-6, (20, 4) = 0.7221359286521267e-7, (20, 5) = -0.756490724910656e-7, (21, 1) = 1.071483064754158, (21, 2) = 0.2162423610813038e-6, (21, 3) = -0.25593520469778174e-6, (21, 4) = 0.26367855391509727e-7, (21, 5) = -0.3099182802156362e-7, (22, 1) = 1.07148318136988, (22, 2) = 0.6124869999887661e-7, (22, 3) = -0.10415162185182523e-6, (22, 4) = 0.7586701144665916e-8, (22, 5) = -0.12697548109268844e-7, (23, 1) = 1.0714832046525464, (23, 2) = .0, (23, 3) = -0.414339042389871e-7, (23, 4) = .0, (23, 5) = -0.5307519484383215e-8}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .7509958992140092, (1, 3) = -1.0, (1, 4) = -.5766182177889736, (1, 5) = .0, (2, 1) = .345717339320025, (2, 2) = .11748530886258848, (2, 3) = -.44685722355458307, (2, 4) = -.42619398711861173, (2, 5) = .2456380242084213, (3, 1) = .3295368928873986, (3, 2) = -.10281256306809654, (3, 3) = -0.9786766510705683e-1, (3, 4) = -.22929557876687195, (3, 5) = .1827710770439118, (4, 1) = .2211740580910692, (4, 2) = -.12239573074044155, (4, 3) = 0.26569430715397205e-1, (4, 4) = -.10715356554772232, (4, 5) = 0.9622754869041322e-1, (5, 1) = .1264140268653532, (5, 2) = -0.8591949919337281e-1, (5, 3) = 0.4505713786209132e-1, (5, 4) = -0.4672290447819592e-1, (5, 5) = 0.44058134414995835e-1, (6, 1) = 0.6583176447988233e-1, (6, 2) = -0.4973034058218495e-1, (6, 3) = 0.332224698170035e-1, (6, 4) = -0.1969778835995821e-1, (6, 5) = 0.18945794068761176e-1, (7, 1) = 0.32315267535371534e-1, (7, 2) = -0.2600272586003493e-1, (7, 3) = 0.19495025439737884e-1, (7, 4) = -0.8174310046940966e-2, (7, 5) = 0.792388079531917e-2, (8, 1) = 0.15247583407686798e-1, (8, 2) = -0.12786769213836738e-1, (8, 3) = 0.10247087352154351e-1, (8, 4) = -0.3368066407962972e-2, (8, 5) = 0.3274729438901535e-2, (9, 1) = 0.6998105041282296e-2, (9, 2) = -0.604035420324911e-2, (9, 3) = 0.5052618825463968e-2, (9, 4) = -0.13833280384499146e-2, (9, 5) = 0.13465343117974211e-2, (10, 1) = 0.31478225677167735e-2, (10, 2) = -0.2774978205981712e-2, (10, 3) = 0.2390999068816236e-2, (10, 4) = -0.5673463700191876e-3, (10, 5) = 0.5524949194085244e-3, (11, 1) = 0.13945650673762352e-2, (11, 2) = -0.12492766558546968e-2, (11, 3) = 0.1099873594304329e-2, (11, 4) = -0.23253747538797784e-3, (11, 5) = 0.22648713664049123e-3, (12, 1) = 0.6105700389362067e-3, (12, 2) = -0.553893319523471e-3, (12, 3) = 0.495675152838582e-3, (12, 4) = -0.9528435644133216e-4, (12, 5) = 0.9281083066054085e-4, (13, 1) = 0.26480452107368317e-3, (13, 2) = -0.24268469519682714e-3, (13, 3) = 0.21995944221136622e-3, (13, 4) = -0.39040038537364915e-4, (13, 5) = 0.3802744922108661e-4, (14, 1) = 0.11394909512081752e-3, (14, 2) = -0.10532867430154103e-3, (14, 3) = 0.9644275586103112e-4, (14, 4) = -0.15995006093854115e-4, (14, 5) = 0.15580272849724842e-4, (15, 1) = 0.4870000930855666e-4, (15, 2) = -0.45361559105776056e-4, (15, 3) = 0.41882130392897214e-4, (15, 4) = -0.655308793716169e-5, (15, 5) = 0.6383193495979208e-5, (16, 1) = 0.20679444144369147e-4, (16, 2) = -0.1941000219193855e-4, (16, 3) = 0.18046766192933517e-4, (16, 4) = -0.26847296756546684e-5, (16, 5) = 0.26151287212238395e-5, (17, 1) = 0.8718850547396554e-5, (17, 2) = -0.8259728398401262e-5, (17, 3) = 0.7726423999999988e-5, (17, 4) = -0.10999141617991744e-5, (17, 5) = 0.1071399573515949e-5, (18, 1) = 0.3640252978905283e-5, (18, 2) = -0.3497402269851553e-5, (18, 3) = 0.32902284142233035e-5, (18, 4) = -0.45063567228372506e-6, (18, 5) = 0.43895327171989055e-6, (19, 1) = 0.14944389063713663e-5, (19, 2) = -0.14735566530371413e-5, (19, 3) = 0.13947933808207162e-5, (19, 4) = -0.1846330205946365e-6, (19, 5) = 0.1798465459323782e-6, (20, 1) = 0.5925773918561377e-6, (20, 2) = -0.6170979188394264e-6, (20, 3) = 0.5889965143819995e-6, (20, 4) = -0.756490724910656e-7, (20, 5) = 0.7368792426442866e-7, (21, 1) = 0.2162423610813038e-6, (21, 2) = -0.25593520469778174e-6, (21, 3) = 0.24786242887731095e-6, (21, 4) = -0.3099182802156362e-7, (21, 5) = 0.3018838597520553e-7, (22, 1) = 0.6124869999887661e-7, (22, 2) = -0.10415162185182523e-6, (22, 3) = 0.10401001373336376e-6, (22, 4) = -0.12697548109268844e-7, (22, 5) = 0.12368372462174604e-7, (23, 1) = .0, (23, 2) = -0.414339042389871e-7, (23, 3) = 0.4439573249525663e-7, (23, 4) = -0.5307519484383215e-8, (23, 5) = 0.5169925441711597e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.18677723346185155e-6, (1, 4) = .0, (1, 5) = -0.1601034189830942e-6, (2, 1) = 0.37448226506023734e-7, (2, 2) = -0.4882419193663561e-8, (2, 3) = 0.32590922758163096e-7, (2, 4) = 0.8384642286135039e-8, (2, 5) = -0.3822989163192259e-7, (3, 1) = 0.4178076522983118e-7, (3, 2) = -0.32454728940560626e-7, (3, 3) = 0.5559818911848743e-7, (3, 4) = 0.255368475385125e-7, (3, 5) = -0.26372934101735208e-7, (4, 1) = -0.3503349256133378e-8, (4, 2) = 0.23271413239470415e-7, (4, 3) = -0.13109277388977377e-7, (4, 4) = 0.1940395871477904e-7, (4, 5) = -0.21150015818914884e-7, (5, 1) = 0.9049822894255894e-8, (5, 2) = 0.2044098278596014e-7, (5, 3) = -0.23457165838090578e-7, (5, 4) = 0.2721022646410278e-8, (5, 5) = -0.3786091636826618e-8, (6, 1) = 0.27051273759362853e-7, (6, 2) = 0.15343716259627215e-9, (6, 3) = -0.21958032487259045e-8, (6, 4) = -0.4159511453386257e-9, (6, 5) = 0.38101170586747216e-10, (7, 1) = 0.29235514018364573e-7, (7, 2) = -0.453106337656716e-8, (7, 3) = 0.46319249349793395e-8, (7, 4) = 0.46342814231151797e-9, (7, 5) = -0.6792806203548744e-9, (8, 1) = 0.26054556255110013e-7, (8, 2) = -0.1882133375224601e-8, (8, 3) = 0.2244789452496081e-8, (8, 4) = 0.711835820669783e-9, (8, 5) = -0.8568477954792043e-9, (9, 1) = 0.24106962716022037e-7, (9, 2) = 0.1629685214904445e-9, (9, 3) = -0.11146494499834733e-9, (9, 4) = 0.45110688737061194e-9, (9, 5) = -0.539236754168219e-9, (10, 1) = 0.2374177391716608e-7, (10, 2) = 0.5860236135721297e-9, (10, 3) = -0.7196114662102999e-9, (10, 4) = 0.18313053413689276e-9, (10, 5) = -0.23112721605478909e-9, (11, 1) = 0.23938814887888642e-7, (11, 2) = 0.34670384490097316e-9, (11, 3) = -0.499387007098935e-9, (11, 4) = 0.40264060755003194e-10, (11, 5) = -0.6396528893681144e-10, (12, 1) = 0.2413280997412847e-7, (12, 2) = 0.8123434213412095e-10, (12, 3) = -0.18766851557521373e-9, (12, 4) = -0.10028889791867737e-10, (12, 5) = -0.5607571181840299e-12, (13, 1) = 0.24205166580449604e-7, (13, 2) = -0.4873554507228097e-10, (13, 3) = -0.9122645013749574e-11, (13, 4) = -0.1774384229814944e-10, (13, 5) = 0.13554216810388484e-10, (14, 1) = 0.24197923253315855e-7, (14, 2) = -0.7644103795235015e-10, (14, 3) = 0.5059366630228127e-10, (14, 4) = -0.12500071087031085e-10, (14, 5) = 0.11123935740845305e-10, (15, 1) = 0.24164459411748233e-7, (15, 2) = -0.6066740320325875e-10, (15, 3) = 0.5144731921398412e-10, (15, 4) = -0.63139041944452e-11, (15, 5) = 0.6018851574113935e-11, (16, 1) = 0.24133003199149926e-7, (16, 2) = -0.36959226456229056e-10, (16, 3) = 0.34807094444056334e-10, (16, 4) = -0.2296584459403134e-11, (16, 5) = 0.2328976704823776e-11, (17, 1) = 0.24111780059612412e-7, (17, 2) = -0.1873228504203057e-10, (17, 3) = 0.18878272014729034e-10, (17, 4) = -0.33241174545583766e-12, (17, 5) = 0.40568885552430346e-12, (18, 1) = 0.24099883385166445e-7, (18, 2) = -0.7930627600316472e-11, (18, 3) = 0.8419004595137473e-11, (18, 4) = 0.3767477185747604e-12, (18, 5) = -0.34832143812623605e-12, (19, 1) = 0.2409407001294113e-7, (19, 2) = -0.26201105239283355e-11, (19, 3) = 0.2849865664815142e-11, (19, 4) = 0.485146485573298e-12, (19, 5) = -0.5118521121703797e-12, (20, 1) = 0.24091528694372805e-7, (20, 2) = -0.4820658103323563e-12, (20, 3) = 0.3930534221642779e-12, (20, 4) = 0.37341039360175125e-12, (20, 5) = -0.4432984456493013e-12, (21, 1) = 0.24090485353105713e-7, (21, 2) = 0.12932248130697764e-12, (21, 3) = -0.4349598146471398e-12, (21, 4) = 0.22003866786553054e-12, (21, 5) = -0.31866839336921104e-12, (22, 1) = 0.24090016159892753e-7, (22, 2) = 0.14345040328921917e-12, (22, 3) = -0.5483809312163577e-12, (22, 4) = 0.9076616249531766e-13, (22, 5) = -0.20691039898422648e-12, (23, 1) = 0.24089729356345837e-7, (23, 2) = .0, (23, 3) = -0.4163274954165759e-12, (23, 4) = .0, (23, 5) = -0.12614313243075443e-12}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187980970662, (2) = 18446884187980970838, (3) = 18446884187980971014, (4) = 18446884187980971190, (5) = 18446884187980971366, (6) = 18446884187980971542}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else g := pointto(data[2][2]); return ('g')(y) end if end if; try res := solnproc(outpoint); res[2] catch: error  end try end proc, D(g) = proc (y) local res, data, solnproc, `D(g)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .7509958992140092, (1, 4) = 1.0, (1, 5) = -.5766182177889736, (2, 1) = .19294506823253071, (2, 2) = .345717339320025, (2, 3) = .11748530886258848, (2, 4) = .5437094913262883, (2, 5) = -.42619398711861173, (3, 1) = .5054078147971317, (3, 2) = .3295368928873986, (3, 3) = -.10281256306809654, (3, 4) = .25842450171487663, (3, 5) = -.22929557876687195, (4, 1) = .7517816685489124, (4, 2) = .2211740580910692, (4, 3) = -.12239573074044155, (4, 4) = .11436339993638699, (4, 5) = -.10715356554772232, (5, 1) = .9054483747328635, (5, 2) = .1264140268653532, (5, 3) = -0.8591949919337281e-1, (5, 4) = 0.48719039228723914e-1, (5, 5) = -0.4672290447819592e-1, (6, 1) = .9900111442791364, (6, 2) = 0.6583176447988233e-1, (6, 3) = -0.4973034058218495e-1, (6, 4) = 0.20344942782691302e-1, (6, 5) = -0.1969778835995821e-1, (7, 1) = 1.0330480370810036, (7, 2) = 0.32315267535371534e-1, (7, 3) = -0.2600272586003493e-1, (7, 4) = 0.841131598460929e-2, (7, 5) = -0.8174310046940966e-2, (8, 1) = 1.0538493557885784, (8, 2) = 0.15247583407686798e-1, (8, 3) = -0.12786769213836738e-1, (8, 4) = 0.3460729946239088e-2, (8, 5) = -0.3368066407962972e-2, (9, 1) = 1.0635555317661158, (9, 2) = 0.6998105041282296e-2, (9, 3) = -0.604035420324911e-2, (9, 4) = 0.14206067753971528e-2, (9, 5) = -0.13833280384499146e-2, (10, 1) = 1.067973284021565, (10, 2) = 0.31478225677167735e-2, (10, 3) = -0.2774978205981712e-2, (10, 4) = 0.582512305832151e-3, (10, 5) = -0.5673463700191876e-3, (11, 1) = 1.0699476410036053, (11, 2) = 0.13945650673762352e-2, (11, 3) = -0.12492766558546968e-2, (11, 4) = 0.23873182831542274e-3, (11, 5) = -0.23253747538797784e-3, (12, 1) = 1.070817852106119, (12, 2) = 0.6105700389362067e-3, (12, 3) = -0.553893319523471e-3, (12, 4) = 0.9781649764191596e-4, (12, 5) = -0.9528435644133216e-4, (13, 1) = 1.071197262363775, (13, 2) = 0.26480452107368317e-3, (13, 3) = -0.24268469519682714e-3, (13, 4) = 0.4007386033544328e-4, (13, 5) = -0.39040038537364915e-4, (14, 1) = 1.0713612440610472, (14, 2) = 0.11394909512081752e-3, (14, 3) = -0.10532867430154103e-3, (14, 4) = 0.16415288070247586e-4, (14, 5) = -0.15995006093854115e-4, (15, 1) = 1.0714315982101714, (15, 2) = 0.4870000930855666e-4, (15, 3) = -0.45361559105776056e-4, (15, 4) = 0.6722049068016235e-5, (15, 5) = -0.655308793716169e-5, (16, 1) = 1.071461583562454, (16, 2) = 0.20679444144369147e-4, (16, 3) = -0.1941000219193855e-4, (16, 4) = 0.2750733132001786e-5, (16, 5) = -0.26847296756546684e-5, (17, 1) = 1.0714742787121994, (17, 2) = 0.8718850547396554e-5, (17, 3) = -0.8259728398401262e-5, (17, 4) = 0.11237385463905423e-5, (17, 5) = -0.10999141617991744e-5, (18, 1) = 1.0714796105551125, (18, 2) = 0.3640252978905283e-5, (18, 3) = -0.3497402269851553e-5, (18, 4) = 0.45718005927355556e-6, (18, 5) = -0.45063567228372506e-6, (19, 1) = 1.0714818225105625, (19, 2) = 0.14944389063713663e-5, (19, 3) = -0.14735566530371413e-5, (19, 4) = 0.18409802069572952e-6, (19, 5) = -0.1846330205946365e-6, (20, 1) = 1.0714827192138023, (20, 2) = 0.5925773918561377e-6, (20, 3) = -0.6170979188394264e-6, (20, 4) = 0.7221359286521267e-7, (20, 5) = -0.756490724910656e-7, (21, 1) = 1.071483064754158, (21, 2) = 0.2162423610813038e-6, (21, 3) = -0.25593520469778174e-6, (21, 4) = 0.26367855391509727e-7, (21, 5) = -0.3099182802156362e-7, (22, 1) = 1.07148318136988, (22, 2) = 0.6124869999887661e-7, (22, 3) = -0.10415162185182523e-6, (22, 4) = 0.7586701144665916e-8, (22, 5) = -0.12697548109268844e-7, (23, 1) = 1.0714832046525464, (23, 2) = .0, (23, 3) = -0.414339042389871e-7, (23, 4) = .0, (23, 5) = -0.5307519484383215e-8}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .7509958992140092, (1, 3) = -1.0, (1, 4) = -.5766182177889736, (1, 5) = .0, (2, 1) = .345717339320025, (2, 2) = .11748530886258848, (2, 3) = -.44685722355458307, (2, 4) = -.42619398711861173, (2, 5) = .2456380242084213, (3, 1) = .3295368928873986, (3, 2) = -.10281256306809654, (3, 3) = -0.9786766510705683e-1, (3, 4) = -.22929557876687195, (3, 5) = .1827710770439118, (4, 1) = .2211740580910692, (4, 2) = -.12239573074044155, (4, 3) = 0.26569430715397205e-1, (4, 4) = -.10715356554772232, (4, 5) = 0.9622754869041322e-1, (5, 1) = .1264140268653532, (5, 2) = -0.8591949919337281e-1, (5, 3) = 0.4505713786209132e-1, (5, 4) = -0.4672290447819592e-1, (5, 5) = 0.44058134414995835e-1, (6, 1) = 0.6583176447988233e-1, (6, 2) = -0.4973034058218495e-1, (6, 3) = 0.332224698170035e-1, (6, 4) = -0.1969778835995821e-1, (6, 5) = 0.18945794068761176e-1, (7, 1) = 0.32315267535371534e-1, (7, 2) = -0.2600272586003493e-1, (7, 3) = 0.19495025439737884e-1, (7, 4) = -0.8174310046940966e-2, (7, 5) = 0.792388079531917e-2, (8, 1) = 0.15247583407686798e-1, (8, 2) = -0.12786769213836738e-1, (8, 3) = 0.10247087352154351e-1, (8, 4) = -0.3368066407962972e-2, (8, 5) = 0.3274729438901535e-2, (9, 1) = 0.6998105041282296e-2, (9, 2) = -0.604035420324911e-2, (9, 3) = 0.5052618825463968e-2, (9, 4) = -0.13833280384499146e-2, (9, 5) = 0.13465343117974211e-2, (10, 1) = 0.31478225677167735e-2, (10, 2) = -0.2774978205981712e-2, (10, 3) = 0.2390999068816236e-2, (10, 4) = -0.5673463700191876e-3, (10, 5) = 0.5524949194085244e-3, (11, 1) = 0.13945650673762352e-2, (11, 2) = -0.12492766558546968e-2, (11, 3) = 0.1099873594304329e-2, (11, 4) = -0.23253747538797784e-3, (11, 5) = 0.22648713664049123e-3, (12, 1) = 0.6105700389362067e-3, (12, 2) = -0.553893319523471e-3, (12, 3) = 0.495675152838582e-3, (12, 4) = -0.9528435644133216e-4, (12, 5) = 0.9281083066054085e-4, (13, 1) = 0.26480452107368317e-3, (13, 2) = -0.24268469519682714e-3, (13, 3) = 0.21995944221136622e-3, (13, 4) = -0.39040038537364915e-4, (13, 5) = 0.3802744922108661e-4, (14, 1) = 0.11394909512081752e-3, (14, 2) = -0.10532867430154103e-3, (14, 3) = 0.9644275586103112e-4, (14, 4) = -0.15995006093854115e-4, (14, 5) = 0.15580272849724842e-4, (15, 1) = 0.4870000930855666e-4, (15, 2) = -0.45361559105776056e-4, (15, 3) = 0.41882130392897214e-4, (15, 4) = -0.655308793716169e-5, (15, 5) = 0.6383193495979208e-5, (16, 1) = 0.20679444144369147e-4, (16, 2) = -0.1941000219193855e-4, (16, 3) = 0.18046766192933517e-4, (16, 4) = -0.26847296756546684e-5, (16, 5) = 0.26151287212238395e-5, (17, 1) = 0.8718850547396554e-5, (17, 2) = -0.8259728398401262e-5, (17, 3) = 0.7726423999999988e-5, (17, 4) = -0.10999141617991744e-5, (17, 5) = 0.1071399573515949e-5, (18, 1) = 0.3640252978905283e-5, (18, 2) = -0.3497402269851553e-5, (18, 3) = 0.32902284142233035e-5, (18, 4) = -0.45063567228372506e-6, (18, 5) = 0.43895327171989055e-6, (19, 1) = 0.14944389063713663e-5, (19, 2) = -0.14735566530371413e-5, (19, 3) = 0.13947933808207162e-5, (19, 4) = -0.1846330205946365e-6, (19, 5) = 0.1798465459323782e-6, (20, 1) = 0.5925773918561377e-6, (20, 2) = -0.6170979188394264e-6, (20, 3) = 0.5889965143819995e-6, (20, 4) = -0.756490724910656e-7, (20, 5) = 0.7368792426442866e-7, (21, 1) = 0.2162423610813038e-6, (21, 2) = -0.25593520469778174e-6, (21, 3) = 0.24786242887731095e-6, (21, 4) = -0.3099182802156362e-7, (21, 5) = 0.3018838597520553e-7, (22, 1) = 0.6124869999887661e-7, (22, 2) = -0.10415162185182523e-6, (22, 3) = 0.10401001373336376e-6, (22, 4) = -0.12697548109268844e-7, (22, 5) = 0.12368372462174604e-7, (23, 1) = .0, (23, 2) = -0.414339042389871e-7, (23, 3) = 0.4439573249525663e-7, (23, 4) = -0.5307519484383215e-8, (23, 5) = 0.5169925441711597e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.18677723346185155e-6, (1, 4) = .0, (1, 5) = -0.1601034189830942e-6, (2, 1) = 0.37448226506023734e-7, (2, 2) = -0.4882419193663561e-8, (2, 3) = 0.32590922758163096e-7, (2, 4) = 0.8384642286135039e-8, (2, 5) = -0.3822989163192259e-7, (3, 1) = 0.4178076522983118e-7, (3, 2) = -0.32454728940560626e-7, (3, 3) = 0.5559818911848743e-7, (3, 4) = 0.255368475385125e-7, (3, 5) = -0.26372934101735208e-7, (4, 1) = -0.3503349256133378e-8, (4, 2) = 0.23271413239470415e-7, (4, 3) = -0.13109277388977377e-7, (4, 4) = 0.1940395871477904e-7, (4, 5) = -0.21150015818914884e-7, (5, 1) = 0.9049822894255894e-8, (5, 2) = 0.2044098278596014e-7, (5, 3) = -0.23457165838090578e-7, (5, 4) = 0.2721022646410278e-8, (5, 5) = -0.3786091636826618e-8, (6, 1) = 0.27051273759362853e-7, (6, 2) = 0.15343716259627215e-9, (6, 3) = -0.21958032487259045e-8, (6, 4) = -0.4159511453386257e-9, (6, 5) = 0.38101170586747216e-10, (7, 1) = 0.29235514018364573e-7, (7, 2) = -0.453106337656716e-8, (7, 3) = 0.46319249349793395e-8, (7, 4) = 0.46342814231151797e-9, (7, 5) = -0.6792806203548744e-9, (8, 1) = 0.26054556255110013e-7, (8, 2) = -0.1882133375224601e-8, (8, 3) = 0.2244789452496081e-8, (8, 4) = 0.711835820669783e-9, (8, 5) = -0.8568477954792043e-9, (9, 1) = 0.24106962716022037e-7, (9, 2) = 0.1629685214904445e-9, (9, 3) = -0.11146494499834733e-9, (9, 4) = 0.45110688737061194e-9, (9, 5) = -0.539236754168219e-9, (10, 1) = 0.2374177391716608e-7, (10, 2) = 0.5860236135721297e-9, (10, 3) = -0.7196114662102999e-9, (10, 4) = 0.18313053413689276e-9, (10, 5) = -0.23112721605478909e-9, (11, 1) = 0.23938814887888642e-7, (11, 2) = 0.34670384490097316e-9, (11, 3) = -0.499387007098935e-9, (11, 4) = 0.40264060755003194e-10, (11, 5) = -0.6396528893681144e-10, (12, 1) = 0.2413280997412847e-7, (12, 2) = 0.8123434213412095e-10, (12, 3) = -0.18766851557521373e-9, (12, 4) = -0.10028889791867737e-10, (12, 5) = -0.5607571181840299e-12, (13, 1) = 0.24205166580449604e-7, (13, 2) = -0.4873554507228097e-10, (13, 3) = -0.9122645013749574e-11, (13, 4) = -0.1774384229814944e-10, (13, 5) = 0.13554216810388484e-10, (14, 1) = 0.24197923253315855e-7, (14, 2) = -0.7644103795235015e-10, (14, 3) = 0.5059366630228127e-10, (14, 4) = -0.12500071087031085e-10, (14, 5) = 0.11123935740845305e-10, (15, 1) = 0.24164459411748233e-7, (15, 2) = -0.6066740320325875e-10, (15, 3) = 0.5144731921398412e-10, (15, 4) = -0.63139041944452e-11, (15, 5) = 0.6018851574113935e-11, (16, 1) = 0.24133003199149926e-7, (16, 2) = -0.36959226456229056e-10, (16, 3) = 0.34807094444056334e-10, (16, 4) = -0.2296584459403134e-11, (16, 5) = 0.2328976704823776e-11, (17, 1) = 0.24111780059612412e-7, (17, 2) = -0.1873228504203057e-10, (17, 3) = 0.18878272014729034e-10, (17, 4) = -0.33241174545583766e-12, (17, 5) = 0.40568885552430346e-12, (18, 1) = 0.24099883385166445e-7, (18, 2) = -0.7930627600316472e-11, (18, 3) = 0.8419004595137473e-11, (18, 4) = 0.3767477185747604e-12, (18, 5) = -0.34832143812623605e-12, (19, 1) = 0.2409407001294113e-7, (19, 2) = -0.26201105239283355e-11, (19, 3) = 0.2849865664815142e-11, (19, 4) = 0.485146485573298e-12, (19, 5) = -0.5118521121703797e-12, (20, 1) = 0.24091528694372805e-7, (20, 2) = -0.4820658103323563e-12, (20, 3) = 0.3930534221642779e-12, (20, 4) = 0.37341039360175125e-12, (20, 5) = -0.4432984456493013e-12, (21, 1) = 0.24090485353105713e-7, (21, 2) = 0.12932248130697764e-12, (21, 3) = -0.4349598146471398e-12, (21, 4) = 0.22003866786553054e-12, (21, 5) = -0.31866839336921104e-12, (22, 1) = 0.24090016159892753e-7, (22, 2) = 0.14345040328921917e-12, (22, 3) = -0.5483809312163577e-12, (22, 4) = 0.9076616249531766e-13, (22, 5) = -0.20691039898422648e-12, (23, 1) = 0.24089729356345837e-7, (23, 2) = .0, (23, 3) = -0.4163274954165759e-12, (23, 4) = .0, (23, 5) = -0.12614313243075443e-12}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187980970662, (2) = 18446884187980970838, (3) = 18446884187980971014, (4) = 18446884187980971190, (5) = 18446884187980971366, (6) = 18446884187980971542}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `D(g)` := pointto(data[2][3]); return ('`D(g)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc, (D@@2)(g) = proc (y) local res, data, solnproc, `\`@@\`(D,2)(g)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .7509958992140092, (1, 4) = 1.0, (1, 5) = -.5766182177889736, (2, 1) = .19294506823253071, (2, 2) = .345717339320025, (2, 3) = .11748530886258848, (2, 4) = .5437094913262883, (2, 5) = -.42619398711861173, (3, 1) = .5054078147971317, (3, 2) = .3295368928873986, (3, 3) = -.10281256306809654, (3, 4) = .25842450171487663, (3, 5) = -.22929557876687195, (4, 1) = .7517816685489124, (4, 2) = .2211740580910692, (4, 3) = -.12239573074044155, (4, 4) = .11436339993638699, (4, 5) = -.10715356554772232, (5, 1) = .9054483747328635, (5, 2) = .1264140268653532, (5, 3) = -0.8591949919337281e-1, (5, 4) = 0.48719039228723914e-1, (5, 5) = -0.4672290447819592e-1, (6, 1) = .9900111442791364, (6, 2) = 0.6583176447988233e-1, (6, 3) = -0.4973034058218495e-1, (6, 4) = 0.20344942782691302e-1, (6, 5) = -0.1969778835995821e-1, (7, 1) = 1.0330480370810036, (7, 2) = 0.32315267535371534e-1, (7, 3) = -0.2600272586003493e-1, (7, 4) = 0.841131598460929e-2, (7, 5) = -0.8174310046940966e-2, (8, 1) = 1.0538493557885784, (8, 2) = 0.15247583407686798e-1, (8, 3) = -0.12786769213836738e-1, (8, 4) = 0.3460729946239088e-2, (8, 5) = -0.3368066407962972e-2, (9, 1) = 1.0635555317661158, (9, 2) = 0.6998105041282296e-2, (9, 3) = -0.604035420324911e-2, (9, 4) = 0.14206067753971528e-2, (9, 5) = -0.13833280384499146e-2, (10, 1) = 1.067973284021565, (10, 2) = 0.31478225677167735e-2, (10, 3) = -0.2774978205981712e-2, (10, 4) = 0.582512305832151e-3, (10, 5) = -0.5673463700191876e-3, (11, 1) = 1.0699476410036053, (11, 2) = 0.13945650673762352e-2, (11, 3) = -0.12492766558546968e-2, (11, 4) = 0.23873182831542274e-3, (11, 5) = -0.23253747538797784e-3, (12, 1) = 1.070817852106119, (12, 2) = 0.6105700389362067e-3, (12, 3) = -0.553893319523471e-3, (12, 4) = 0.9781649764191596e-4, (12, 5) = -0.9528435644133216e-4, (13, 1) = 1.071197262363775, (13, 2) = 0.26480452107368317e-3, (13, 3) = -0.24268469519682714e-3, (13, 4) = 0.4007386033544328e-4, (13, 5) = -0.39040038537364915e-4, (14, 1) = 1.0713612440610472, (14, 2) = 0.11394909512081752e-3, (14, 3) = -0.10532867430154103e-3, (14, 4) = 0.16415288070247586e-4, (14, 5) = -0.15995006093854115e-4, (15, 1) = 1.0714315982101714, (15, 2) = 0.4870000930855666e-4, (15, 3) = -0.45361559105776056e-4, (15, 4) = 0.6722049068016235e-5, (15, 5) = -0.655308793716169e-5, (16, 1) = 1.071461583562454, (16, 2) = 0.20679444144369147e-4, (16, 3) = -0.1941000219193855e-4, (16, 4) = 0.2750733132001786e-5, (16, 5) = -0.26847296756546684e-5, (17, 1) = 1.0714742787121994, (17, 2) = 0.8718850547396554e-5, (17, 3) = -0.8259728398401262e-5, (17, 4) = 0.11237385463905423e-5, (17, 5) = -0.10999141617991744e-5, (18, 1) = 1.0714796105551125, (18, 2) = 0.3640252978905283e-5, (18, 3) = -0.3497402269851553e-5, (18, 4) = 0.45718005927355556e-6, (18, 5) = -0.45063567228372506e-6, (19, 1) = 1.0714818225105625, (19, 2) = 0.14944389063713663e-5, (19, 3) = -0.14735566530371413e-5, (19, 4) = 0.18409802069572952e-6, (19, 5) = -0.1846330205946365e-6, (20, 1) = 1.0714827192138023, (20, 2) = 0.5925773918561377e-6, (20, 3) = -0.6170979188394264e-6, (20, 4) = 0.7221359286521267e-7, (20, 5) = -0.756490724910656e-7, (21, 1) = 1.071483064754158, (21, 2) = 0.2162423610813038e-6, (21, 3) = -0.25593520469778174e-6, (21, 4) = 0.26367855391509727e-7, (21, 5) = -0.3099182802156362e-7, (22, 1) = 1.07148318136988, (22, 2) = 0.6124869999887661e-7, (22, 3) = -0.10415162185182523e-6, (22, 4) = 0.7586701144665916e-8, (22, 5) = -0.12697548109268844e-7, (23, 1) = 1.0714832046525464, (23, 2) = .0, (23, 3) = -0.414339042389871e-7, (23, 4) = .0, (23, 5) = -0.5307519484383215e-8}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .7509958992140092, (1, 3) = -1.0, (1, 4) = -.5766182177889736, (1, 5) = .0, (2, 1) = .345717339320025, (2, 2) = .11748530886258848, (2, 3) = -.44685722355458307, (2, 4) = -.42619398711861173, (2, 5) = .2456380242084213, (3, 1) = .3295368928873986, (3, 2) = -.10281256306809654, (3, 3) = -0.9786766510705683e-1, (3, 4) = -.22929557876687195, (3, 5) = .1827710770439118, (4, 1) = .2211740580910692, (4, 2) = -.12239573074044155, (4, 3) = 0.26569430715397205e-1, (4, 4) = -.10715356554772232, (4, 5) = 0.9622754869041322e-1, (5, 1) = .1264140268653532, (5, 2) = -0.8591949919337281e-1, (5, 3) = 0.4505713786209132e-1, (5, 4) = -0.4672290447819592e-1, (5, 5) = 0.44058134414995835e-1, (6, 1) = 0.6583176447988233e-1, (6, 2) = -0.4973034058218495e-1, (6, 3) = 0.332224698170035e-1, (6, 4) = -0.1969778835995821e-1, (6, 5) = 0.18945794068761176e-1, (7, 1) = 0.32315267535371534e-1, (7, 2) = -0.2600272586003493e-1, (7, 3) = 0.19495025439737884e-1, (7, 4) = -0.8174310046940966e-2, (7, 5) = 0.792388079531917e-2, (8, 1) = 0.15247583407686798e-1, (8, 2) = -0.12786769213836738e-1, (8, 3) = 0.10247087352154351e-1, (8, 4) = -0.3368066407962972e-2, (8, 5) = 0.3274729438901535e-2, (9, 1) = 0.6998105041282296e-2, (9, 2) = -0.604035420324911e-2, (9, 3) = 0.5052618825463968e-2, (9, 4) = -0.13833280384499146e-2, (9, 5) = 0.13465343117974211e-2, (10, 1) = 0.31478225677167735e-2, (10, 2) = -0.2774978205981712e-2, (10, 3) = 0.2390999068816236e-2, (10, 4) = -0.5673463700191876e-3, (10, 5) = 0.5524949194085244e-3, (11, 1) = 0.13945650673762352e-2, (11, 2) = -0.12492766558546968e-2, (11, 3) = 0.1099873594304329e-2, (11, 4) = -0.23253747538797784e-3, (11, 5) = 0.22648713664049123e-3, (12, 1) = 0.6105700389362067e-3, (12, 2) = -0.553893319523471e-3, (12, 3) = 0.495675152838582e-3, (12, 4) = -0.9528435644133216e-4, (12, 5) = 0.9281083066054085e-4, (13, 1) = 0.26480452107368317e-3, (13, 2) = -0.24268469519682714e-3, (13, 3) = 0.21995944221136622e-3, (13, 4) = -0.39040038537364915e-4, (13, 5) = 0.3802744922108661e-4, (14, 1) = 0.11394909512081752e-3, (14, 2) = -0.10532867430154103e-3, (14, 3) = 0.9644275586103112e-4, (14, 4) = -0.15995006093854115e-4, (14, 5) = 0.15580272849724842e-4, (15, 1) = 0.4870000930855666e-4, (15, 2) = -0.45361559105776056e-4, (15, 3) = 0.41882130392897214e-4, (15, 4) = -0.655308793716169e-5, (15, 5) = 0.6383193495979208e-5, (16, 1) = 0.20679444144369147e-4, (16, 2) = -0.1941000219193855e-4, (16, 3) = 0.18046766192933517e-4, (16, 4) = -0.26847296756546684e-5, (16, 5) = 0.26151287212238395e-5, (17, 1) = 0.8718850547396554e-5, (17, 2) = -0.8259728398401262e-5, (17, 3) = 0.7726423999999988e-5, (17, 4) = -0.10999141617991744e-5, (17, 5) = 0.1071399573515949e-5, (18, 1) = 0.3640252978905283e-5, (18, 2) = -0.3497402269851553e-5, (18, 3) = 0.32902284142233035e-5, (18, 4) = -0.45063567228372506e-6, (18, 5) = 0.43895327171989055e-6, (19, 1) = 0.14944389063713663e-5, (19, 2) = -0.14735566530371413e-5, (19, 3) = 0.13947933808207162e-5, (19, 4) = -0.1846330205946365e-6, (19, 5) = 0.1798465459323782e-6, (20, 1) = 0.5925773918561377e-6, (20, 2) = -0.6170979188394264e-6, (20, 3) = 0.5889965143819995e-6, (20, 4) = -0.756490724910656e-7, (20, 5) = 0.7368792426442866e-7, (21, 1) = 0.2162423610813038e-6, (21, 2) = -0.25593520469778174e-6, (21, 3) = 0.24786242887731095e-6, (21, 4) = -0.3099182802156362e-7, (21, 5) = 0.3018838597520553e-7, (22, 1) = 0.6124869999887661e-7, (22, 2) = -0.10415162185182523e-6, (22, 3) = 0.10401001373336376e-6, (22, 4) = -0.12697548109268844e-7, (22, 5) = 0.12368372462174604e-7, (23, 1) = .0, (23, 2) = -0.414339042389871e-7, (23, 3) = 0.4439573249525663e-7, (23, 4) = -0.5307519484383215e-8, (23, 5) = 0.5169925441711597e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.18677723346185155e-6, (1, 4) = .0, (1, 5) = -0.1601034189830942e-6, (2, 1) = 0.37448226506023734e-7, (2, 2) = -0.4882419193663561e-8, (2, 3) = 0.32590922758163096e-7, (2, 4) = 0.8384642286135039e-8, (2, 5) = -0.3822989163192259e-7, (3, 1) = 0.4178076522983118e-7, (3, 2) = -0.32454728940560626e-7, (3, 3) = 0.5559818911848743e-7, (3, 4) = 0.255368475385125e-7, (3, 5) = -0.26372934101735208e-7, (4, 1) = -0.3503349256133378e-8, (4, 2) = 0.23271413239470415e-7, (4, 3) = -0.13109277388977377e-7, (4, 4) = 0.1940395871477904e-7, (4, 5) = -0.21150015818914884e-7, (5, 1) = 0.9049822894255894e-8, (5, 2) = 0.2044098278596014e-7, (5, 3) = -0.23457165838090578e-7, (5, 4) = 0.2721022646410278e-8, (5, 5) = -0.3786091636826618e-8, (6, 1) = 0.27051273759362853e-7, (6, 2) = 0.15343716259627215e-9, (6, 3) = -0.21958032487259045e-8, (6, 4) = -0.4159511453386257e-9, (6, 5) = 0.38101170586747216e-10, (7, 1) = 0.29235514018364573e-7, (7, 2) = -0.453106337656716e-8, (7, 3) = 0.46319249349793395e-8, (7, 4) = 0.46342814231151797e-9, (7, 5) = -0.6792806203548744e-9, (8, 1) = 0.26054556255110013e-7, (8, 2) = -0.1882133375224601e-8, (8, 3) = 0.2244789452496081e-8, (8, 4) = 0.711835820669783e-9, (8, 5) = -0.8568477954792043e-9, (9, 1) = 0.24106962716022037e-7, (9, 2) = 0.1629685214904445e-9, (9, 3) = -0.11146494499834733e-9, (9, 4) = 0.45110688737061194e-9, (9, 5) = -0.539236754168219e-9, (10, 1) = 0.2374177391716608e-7, (10, 2) = 0.5860236135721297e-9, (10, 3) = -0.7196114662102999e-9, (10, 4) = 0.18313053413689276e-9, (10, 5) = -0.23112721605478909e-9, (11, 1) = 0.23938814887888642e-7, (11, 2) = 0.34670384490097316e-9, (11, 3) = -0.499387007098935e-9, (11, 4) = 0.40264060755003194e-10, (11, 5) = -0.6396528893681144e-10, (12, 1) = 0.2413280997412847e-7, (12, 2) = 0.8123434213412095e-10, (12, 3) = -0.18766851557521373e-9, (12, 4) = -0.10028889791867737e-10, (12, 5) = -0.5607571181840299e-12, (13, 1) = 0.24205166580449604e-7, (13, 2) = -0.4873554507228097e-10, (13, 3) = -0.9122645013749574e-11, (13, 4) = -0.1774384229814944e-10, (13, 5) = 0.13554216810388484e-10, (14, 1) = 0.24197923253315855e-7, (14, 2) = -0.7644103795235015e-10, (14, 3) = 0.5059366630228127e-10, (14, 4) = -0.12500071087031085e-10, (14, 5) = 0.11123935740845305e-10, (15, 1) = 0.24164459411748233e-7, (15, 2) = -0.6066740320325875e-10, (15, 3) = 0.5144731921398412e-10, (15, 4) = -0.63139041944452e-11, (15, 5) = 0.6018851574113935e-11, (16, 1) = 0.24133003199149926e-7, (16, 2) = -0.36959226456229056e-10, (16, 3) = 0.34807094444056334e-10, (16, 4) = -0.2296584459403134e-11, (16, 5) = 0.2328976704823776e-11, (17, 1) = 0.24111780059612412e-7, (17, 2) = -0.1873228504203057e-10, (17, 3) = 0.18878272014729034e-10, (17, 4) = -0.33241174545583766e-12, (17, 5) = 0.40568885552430346e-12, (18, 1) = 0.24099883385166445e-7, (18, 2) = -0.7930627600316472e-11, (18, 3) = 0.8419004595137473e-11, (18, 4) = 0.3767477185747604e-12, (18, 5) = -0.34832143812623605e-12, (19, 1) = 0.2409407001294113e-7, (19, 2) = -0.26201105239283355e-11, (19, 3) = 0.2849865664815142e-11, (19, 4) = 0.485146485573298e-12, (19, 5) = -0.5118521121703797e-12, (20, 1) = 0.24091528694372805e-7, (20, 2) = -0.4820658103323563e-12, (20, 3) = 0.3930534221642779e-12, (20, 4) = 0.37341039360175125e-12, (20, 5) = -0.4432984456493013e-12, (21, 1) = 0.24090485353105713e-7, (21, 2) = 0.12932248130697764e-12, (21, 3) = -0.4349598146471398e-12, (21, 4) = 0.22003866786553054e-12, (21, 5) = -0.31866839336921104e-12, (22, 1) = 0.24090016159892753e-7, (22, 2) = 0.14345040328921917e-12, (22, 3) = -0.5483809312163577e-12, (22, 4) = 0.9076616249531766e-13, (22, 5) = -0.20691039898422648e-12, (23, 1) = 0.24089729356345837e-7, (23, 2) = .0, (23, 3) = -0.4163274954165759e-12, (23, 4) = .0, (23, 5) = -0.12614313243075443e-12}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187980970662, (2) = 18446884187980970838, (3) = 18446884187980971014, (4) = 18446884187980971190, (5) = 18446884187980971366, (6) = 18446884187980971542}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `\`@@\`(D,2)(g)` := pointto(data[2][4]); return ('`\`@@\`(D,2)(g)`')(y) end if end if; try res := solnproc(outpoint); res[4] catch: error  end try end proc, h = proc (y) local res, data, solnproc, h, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .7509958992140092, (1, 4) = 1.0, (1, 5) = -.5766182177889736, (2, 1) = .19294506823253071, (2, 2) = .345717339320025, (2, 3) = .11748530886258848, (2, 4) = .5437094913262883, (2, 5) = -.42619398711861173, (3, 1) = .5054078147971317, (3, 2) = .3295368928873986, (3, 3) = -.10281256306809654, (3, 4) = .25842450171487663, (3, 5) = -.22929557876687195, (4, 1) = .7517816685489124, (4, 2) = .2211740580910692, (4, 3) = -.12239573074044155, (4, 4) = .11436339993638699, (4, 5) = -.10715356554772232, (5, 1) = .9054483747328635, (5, 2) = .1264140268653532, (5, 3) = -0.8591949919337281e-1, (5, 4) = 0.48719039228723914e-1, (5, 5) = -0.4672290447819592e-1, (6, 1) = .9900111442791364, (6, 2) = 0.6583176447988233e-1, (6, 3) = -0.4973034058218495e-1, (6, 4) = 0.20344942782691302e-1, (6, 5) = -0.1969778835995821e-1, (7, 1) = 1.0330480370810036, (7, 2) = 0.32315267535371534e-1, (7, 3) = -0.2600272586003493e-1, (7, 4) = 0.841131598460929e-2, (7, 5) = -0.8174310046940966e-2, (8, 1) = 1.0538493557885784, (8, 2) = 0.15247583407686798e-1, (8, 3) = -0.12786769213836738e-1, (8, 4) = 0.3460729946239088e-2, (8, 5) = -0.3368066407962972e-2, (9, 1) = 1.0635555317661158, (9, 2) = 0.6998105041282296e-2, (9, 3) = -0.604035420324911e-2, (9, 4) = 0.14206067753971528e-2, (9, 5) = -0.13833280384499146e-2, (10, 1) = 1.067973284021565, (10, 2) = 0.31478225677167735e-2, (10, 3) = -0.2774978205981712e-2, (10, 4) = 0.582512305832151e-3, (10, 5) = -0.5673463700191876e-3, (11, 1) = 1.0699476410036053, (11, 2) = 0.13945650673762352e-2, (11, 3) = -0.12492766558546968e-2, (11, 4) = 0.23873182831542274e-3, (11, 5) = -0.23253747538797784e-3, (12, 1) = 1.070817852106119, (12, 2) = 0.6105700389362067e-3, (12, 3) = -0.553893319523471e-3, (12, 4) = 0.9781649764191596e-4, (12, 5) = -0.9528435644133216e-4, (13, 1) = 1.071197262363775, (13, 2) = 0.26480452107368317e-3, (13, 3) = -0.24268469519682714e-3, (13, 4) = 0.4007386033544328e-4, (13, 5) = -0.39040038537364915e-4, (14, 1) = 1.0713612440610472, (14, 2) = 0.11394909512081752e-3, (14, 3) = -0.10532867430154103e-3, (14, 4) = 0.16415288070247586e-4, (14, 5) = -0.15995006093854115e-4, (15, 1) = 1.0714315982101714, (15, 2) = 0.4870000930855666e-4, (15, 3) = -0.45361559105776056e-4, (15, 4) = 0.6722049068016235e-5, (15, 5) = -0.655308793716169e-5, (16, 1) = 1.071461583562454, (16, 2) = 0.20679444144369147e-4, (16, 3) = -0.1941000219193855e-4, (16, 4) = 0.2750733132001786e-5, (16, 5) = -0.26847296756546684e-5, (17, 1) = 1.0714742787121994, (17, 2) = 0.8718850547396554e-5, (17, 3) = -0.8259728398401262e-5, (17, 4) = 0.11237385463905423e-5, (17, 5) = -0.10999141617991744e-5, (18, 1) = 1.0714796105551125, (18, 2) = 0.3640252978905283e-5, (18, 3) = -0.3497402269851553e-5, (18, 4) = 0.45718005927355556e-6, (18, 5) = -0.45063567228372506e-6, (19, 1) = 1.0714818225105625, (19, 2) = 0.14944389063713663e-5, (19, 3) = -0.14735566530371413e-5, (19, 4) = 0.18409802069572952e-6, (19, 5) = -0.1846330205946365e-6, (20, 1) = 1.0714827192138023, (20, 2) = 0.5925773918561377e-6, (20, 3) = -0.6170979188394264e-6, (20, 4) = 0.7221359286521267e-7, (20, 5) = -0.756490724910656e-7, (21, 1) = 1.071483064754158, (21, 2) = 0.2162423610813038e-6, (21, 3) = -0.25593520469778174e-6, (21, 4) = 0.26367855391509727e-7, (21, 5) = -0.3099182802156362e-7, (22, 1) = 1.07148318136988, (22, 2) = 0.6124869999887661e-7, (22, 3) = -0.10415162185182523e-6, (22, 4) = 0.7586701144665916e-8, (22, 5) = -0.12697548109268844e-7, (23, 1) = 1.0714832046525464, (23, 2) = .0, (23, 3) = -0.414339042389871e-7, (23, 4) = .0, (23, 5) = -0.5307519484383215e-8}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .7509958992140092, (1, 3) = -1.0, (1, 4) = -.5766182177889736, (1, 5) = .0, (2, 1) = .345717339320025, (2, 2) = .11748530886258848, (2, 3) = -.44685722355458307, (2, 4) = -.42619398711861173, (2, 5) = .2456380242084213, (3, 1) = .3295368928873986, (3, 2) = -.10281256306809654, (3, 3) = -0.9786766510705683e-1, (3, 4) = -.22929557876687195, (3, 5) = .1827710770439118, (4, 1) = .2211740580910692, (4, 2) = -.12239573074044155, (4, 3) = 0.26569430715397205e-1, (4, 4) = -.10715356554772232, (4, 5) = 0.9622754869041322e-1, (5, 1) = .1264140268653532, (5, 2) = -0.8591949919337281e-1, (5, 3) = 0.4505713786209132e-1, (5, 4) = -0.4672290447819592e-1, (5, 5) = 0.44058134414995835e-1, (6, 1) = 0.6583176447988233e-1, (6, 2) = -0.4973034058218495e-1, (6, 3) = 0.332224698170035e-1, (6, 4) = -0.1969778835995821e-1, (6, 5) = 0.18945794068761176e-1, (7, 1) = 0.32315267535371534e-1, (7, 2) = -0.2600272586003493e-1, (7, 3) = 0.19495025439737884e-1, (7, 4) = -0.8174310046940966e-2, (7, 5) = 0.792388079531917e-2, (8, 1) = 0.15247583407686798e-1, (8, 2) = -0.12786769213836738e-1, (8, 3) = 0.10247087352154351e-1, (8, 4) = -0.3368066407962972e-2, (8, 5) = 0.3274729438901535e-2, (9, 1) = 0.6998105041282296e-2, (9, 2) = -0.604035420324911e-2, (9, 3) = 0.5052618825463968e-2, (9, 4) = -0.13833280384499146e-2, (9, 5) = 0.13465343117974211e-2, (10, 1) = 0.31478225677167735e-2, (10, 2) = -0.2774978205981712e-2, (10, 3) = 0.2390999068816236e-2, (10, 4) = -0.5673463700191876e-3, (10, 5) = 0.5524949194085244e-3, (11, 1) = 0.13945650673762352e-2, (11, 2) = -0.12492766558546968e-2, (11, 3) = 0.1099873594304329e-2, (11, 4) = -0.23253747538797784e-3, (11, 5) = 0.22648713664049123e-3, (12, 1) = 0.6105700389362067e-3, (12, 2) = -0.553893319523471e-3, (12, 3) = 0.495675152838582e-3, (12, 4) = -0.9528435644133216e-4, (12, 5) = 0.9281083066054085e-4, (13, 1) = 0.26480452107368317e-3, (13, 2) = -0.24268469519682714e-3, (13, 3) = 0.21995944221136622e-3, (13, 4) = -0.39040038537364915e-4, (13, 5) = 0.3802744922108661e-4, (14, 1) = 0.11394909512081752e-3, (14, 2) = -0.10532867430154103e-3, (14, 3) = 0.9644275586103112e-4, (14, 4) = -0.15995006093854115e-4, (14, 5) = 0.15580272849724842e-4, (15, 1) = 0.4870000930855666e-4, (15, 2) = -0.45361559105776056e-4, (15, 3) = 0.41882130392897214e-4, (15, 4) = -0.655308793716169e-5, (15, 5) = 0.6383193495979208e-5, (16, 1) = 0.20679444144369147e-4, (16, 2) = -0.1941000219193855e-4, (16, 3) = 0.18046766192933517e-4, (16, 4) = -0.26847296756546684e-5, (16, 5) = 0.26151287212238395e-5, (17, 1) = 0.8718850547396554e-5, (17, 2) = -0.8259728398401262e-5, (17, 3) = 0.7726423999999988e-5, (17, 4) = -0.10999141617991744e-5, (17, 5) = 0.1071399573515949e-5, (18, 1) = 0.3640252978905283e-5, (18, 2) = -0.3497402269851553e-5, (18, 3) = 0.32902284142233035e-5, (18, 4) = -0.45063567228372506e-6, (18, 5) = 0.43895327171989055e-6, (19, 1) = 0.14944389063713663e-5, (19, 2) = -0.14735566530371413e-5, (19, 3) = 0.13947933808207162e-5, (19, 4) = -0.1846330205946365e-6, (19, 5) = 0.1798465459323782e-6, (20, 1) = 0.5925773918561377e-6, (20, 2) = -0.6170979188394264e-6, (20, 3) = 0.5889965143819995e-6, (20, 4) = -0.756490724910656e-7, (20, 5) = 0.7368792426442866e-7, (21, 1) = 0.2162423610813038e-6, (21, 2) = -0.25593520469778174e-6, (21, 3) = 0.24786242887731095e-6, (21, 4) = -0.3099182802156362e-7, (21, 5) = 0.3018838597520553e-7, (22, 1) = 0.6124869999887661e-7, (22, 2) = -0.10415162185182523e-6, (22, 3) = 0.10401001373336376e-6, (22, 4) = -0.12697548109268844e-7, (22, 5) = 0.12368372462174604e-7, (23, 1) = .0, (23, 2) = -0.414339042389871e-7, (23, 3) = 0.4439573249525663e-7, (23, 4) = -0.5307519484383215e-8, (23, 5) = 0.5169925441711597e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.18677723346185155e-6, (1, 4) = .0, (1, 5) = -0.1601034189830942e-6, (2, 1) = 0.37448226506023734e-7, (2, 2) = -0.4882419193663561e-8, (2, 3) = 0.32590922758163096e-7, (2, 4) = 0.8384642286135039e-8, (2, 5) = -0.3822989163192259e-7, (3, 1) = 0.4178076522983118e-7, (3, 2) = -0.32454728940560626e-7, (3, 3) = 0.5559818911848743e-7, (3, 4) = 0.255368475385125e-7, (3, 5) = -0.26372934101735208e-7, (4, 1) = -0.3503349256133378e-8, (4, 2) = 0.23271413239470415e-7, (4, 3) = -0.13109277388977377e-7, (4, 4) = 0.1940395871477904e-7, (4, 5) = -0.21150015818914884e-7, (5, 1) = 0.9049822894255894e-8, (5, 2) = 0.2044098278596014e-7, (5, 3) = -0.23457165838090578e-7, (5, 4) = 0.2721022646410278e-8, (5, 5) = -0.3786091636826618e-8, (6, 1) = 0.27051273759362853e-7, (6, 2) = 0.15343716259627215e-9, (6, 3) = -0.21958032487259045e-8, (6, 4) = -0.4159511453386257e-9, (6, 5) = 0.38101170586747216e-10, (7, 1) = 0.29235514018364573e-7, (7, 2) = -0.453106337656716e-8, (7, 3) = 0.46319249349793395e-8, (7, 4) = 0.46342814231151797e-9, (7, 5) = -0.6792806203548744e-9, (8, 1) = 0.26054556255110013e-7, (8, 2) = -0.1882133375224601e-8, (8, 3) = 0.2244789452496081e-8, (8, 4) = 0.711835820669783e-9, (8, 5) = -0.8568477954792043e-9, (9, 1) = 0.24106962716022037e-7, (9, 2) = 0.1629685214904445e-9, (9, 3) = -0.11146494499834733e-9, (9, 4) = 0.45110688737061194e-9, (9, 5) = -0.539236754168219e-9, (10, 1) = 0.2374177391716608e-7, (10, 2) = 0.5860236135721297e-9, (10, 3) = -0.7196114662102999e-9, (10, 4) = 0.18313053413689276e-9, (10, 5) = -0.23112721605478909e-9, (11, 1) = 0.23938814887888642e-7, (11, 2) = 0.34670384490097316e-9, (11, 3) = -0.499387007098935e-9, (11, 4) = 0.40264060755003194e-10, (11, 5) = -0.6396528893681144e-10, (12, 1) = 0.2413280997412847e-7, (12, 2) = 0.8123434213412095e-10, (12, 3) = -0.18766851557521373e-9, (12, 4) = -0.10028889791867737e-10, (12, 5) = -0.5607571181840299e-12, (13, 1) = 0.24205166580449604e-7, (13, 2) = -0.4873554507228097e-10, (13, 3) = -0.9122645013749574e-11, (13, 4) = -0.1774384229814944e-10, (13, 5) = 0.13554216810388484e-10, (14, 1) = 0.24197923253315855e-7, (14, 2) = -0.7644103795235015e-10, (14, 3) = 0.5059366630228127e-10, (14, 4) = -0.12500071087031085e-10, (14, 5) = 0.11123935740845305e-10, (15, 1) = 0.24164459411748233e-7, (15, 2) = -0.6066740320325875e-10, (15, 3) = 0.5144731921398412e-10, (15, 4) = -0.63139041944452e-11, (15, 5) = 0.6018851574113935e-11, (16, 1) = 0.24133003199149926e-7, (16, 2) = -0.36959226456229056e-10, (16, 3) = 0.34807094444056334e-10, (16, 4) = -0.2296584459403134e-11, (16, 5) = 0.2328976704823776e-11, (17, 1) = 0.24111780059612412e-7, (17, 2) = -0.1873228504203057e-10, (17, 3) = 0.18878272014729034e-10, (17, 4) = -0.33241174545583766e-12, (17, 5) = 0.40568885552430346e-12, (18, 1) = 0.24099883385166445e-7, (18, 2) = -0.7930627600316472e-11, (18, 3) = 0.8419004595137473e-11, (18, 4) = 0.3767477185747604e-12, (18, 5) = -0.34832143812623605e-12, (19, 1) = 0.2409407001294113e-7, (19, 2) = -0.26201105239283355e-11, (19, 3) = 0.2849865664815142e-11, (19, 4) = 0.485146485573298e-12, (19, 5) = -0.5118521121703797e-12, (20, 1) = 0.24091528694372805e-7, (20, 2) = -0.4820658103323563e-12, (20, 3) = 0.3930534221642779e-12, (20, 4) = 0.37341039360175125e-12, (20, 5) = -0.4432984456493013e-12, (21, 1) = 0.24090485353105713e-7, (21, 2) = 0.12932248130697764e-12, (21, 3) = -0.4349598146471398e-12, (21, 4) = 0.22003866786553054e-12, (21, 5) = -0.31866839336921104e-12, (22, 1) = 0.24090016159892753e-7, (22, 2) = 0.14345040328921917e-12, (22, 3) = -0.5483809312163577e-12, (22, 4) = 0.9076616249531766e-13, (22, 5) = -0.20691039898422648e-12, (23, 1) = 0.24089729356345837e-7, (23, 2) = .0, (23, 3) = -0.4163274954165759e-12, (23, 4) = .0, (23, 5) = -0.12614313243075443e-12}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187980970662, (2) = 18446884187980970838, (3) = 18446884187980971014, (4) = 18446884187980971190, (5) = 18446884187980971366, (6) = 18446884187980971542}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else h := pointto(data[2][5]); return ('h')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc, D(h) = proc (y) local res, data, solnproc, `D(h)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .7509958992140092, (1, 4) = 1.0, (1, 5) = -.5766182177889736, (2, 1) = .19294506823253071, (2, 2) = .345717339320025, (2, 3) = .11748530886258848, (2, 4) = .5437094913262883, (2, 5) = -.42619398711861173, (3, 1) = .5054078147971317, (3, 2) = .3295368928873986, (3, 3) = -.10281256306809654, (3, 4) = .25842450171487663, (3, 5) = -.22929557876687195, (4, 1) = .7517816685489124, (4, 2) = .2211740580910692, (4, 3) = -.12239573074044155, (4, 4) = .11436339993638699, (4, 5) = -.10715356554772232, (5, 1) = .9054483747328635, (5, 2) = .1264140268653532, (5, 3) = -0.8591949919337281e-1, (5, 4) = 0.48719039228723914e-1, (5, 5) = -0.4672290447819592e-1, (6, 1) = .9900111442791364, (6, 2) = 0.6583176447988233e-1, (6, 3) = -0.4973034058218495e-1, (6, 4) = 0.20344942782691302e-1, (6, 5) = -0.1969778835995821e-1, (7, 1) = 1.0330480370810036, (7, 2) = 0.32315267535371534e-1, (7, 3) = -0.2600272586003493e-1, (7, 4) = 0.841131598460929e-2, (7, 5) = -0.8174310046940966e-2, (8, 1) = 1.0538493557885784, (8, 2) = 0.15247583407686798e-1, (8, 3) = -0.12786769213836738e-1, (8, 4) = 0.3460729946239088e-2, (8, 5) = -0.3368066407962972e-2, (9, 1) = 1.0635555317661158, (9, 2) = 0.6998105041282296e-2, (9, 3) = -0.604035420324911e-2, (9, 4) = 0.14206067753971528e-2, (9, 5) = -0.13833280384499146e-2, (10, 1) = 1.067973284021565, (10, 2) = 0.31478225677167735e-2, (10, 3) = -0.2774978205981712e-2, (10, 4) = 0.582512305832151e-3, (10, 5) = -0.5673463700191876e-3, (11, 1) = 1.0699476410036053, (11, 2) = 0.13945650673762352e-2, (11, 3) = -0.12492766558546968e-2, (11, 4) = 0.23873182831542274e-3, (11, 5) = -0.23253747538797784e-3, (12, 1) = 1.070817852106119, (12, 2) = 0.6105700389362067e-3, (12, 3) = -0.553893319523471e-3, (12, 4) = 0.9781649764191596e-4, (12, 5) = -0.9528435644133216e-4, (13, 1) = 1.071197262363775, (13, 2) = 0.26480452107368317e-3, (13, 3) = -0.24268469519682714e-3, (13, 4) = 0.4007386033544328e-4, (13, 5) = -0.39040038537364915e-4, (14, 1) = 1.0713612440610472, (14, 2) = 0.11394909512081752e-3, (14, 3) = -0.10532867430154103e-3, (14, 4) = 0.16415288070247586e-4, (14, 5) = -0.15995006093854115e-4, (15, 1) = 1.0714315982101714, (15, 2) = 0.4870000930855666e-4, (15, 3) = -0.45361559105776056e-4, (15, 4) = 0.6722049068016235e-5, (15, 5) = -0.655308793716169e-5, (16, 1) = 1.071461583562454, (16, 2) = 0.20679444144369147e-4, (16, 3) = -0.1941000219193855e-4, (16, 4) = 0.2750733132001786e-5, (16, 5) = -0.26847296756546684e-5, (17, 1) = 1.0714742787121994, (17, 2) = 0.8718850547396554e-5, (17, 3) = -0.8259728398401262e-5, (17, 4) = 0.11237385463905423e-5, (17, 5) = -0.10999141617991744e-5, (18, 1) = 1.0714796105551125, (18, 2) = 0.3640252978905283e-5, (18, 3) = -0.3497402269851553e-5, (18, 4) = 0.45718005927355556e-6, (18, 5) = -0.45063567228372506e-6, (19, 1) = 1.0714818225105625, (19, 2) = 0.14944389063713663e-5, (19, 3) = -0.14735566530371413e-5, (19, 4) = 0.18409802069572952e-6, (19, 5) = -0.1846330205946365e-6, (20, 1) = 1.0714827192138023, (20, 2) = 0.5925773918561377e-6, (20, 3) = -0.6170979188394264e-6, (20, 4) = 0.7221359286521267e-7, (20, 5) = -0.756490724910656e-7, (21, 1) = 1.071483064754158, (21, 2) = 0.2162423610813038e-6, (21, 3) = -0.25593520469778174e-6, (21, 4) = 0.26367855391509727e-7, (21, 5) = -0.3099182802156362e-7, (22, 1) = 1.07148318136988, (22, 2) = 0.6124869999887661e-7, (22, 3) = -0.10415162185182523e-6, (22, 4) = 0.7586701144665916e-8, (22, 5) = -0.12697548109268844e-7, (23, 1) = 1.0714832046525464, (23, 2) = .0, (23, 3) = -0.414339042389871e-7, (23, 4) = .0, (23, 5) = -0.5307519484383215e-8}, datatype = float[8], order = C_order); YP := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .7509958992140092, (1, 3) = -1.0, (1, 4) = -.5766182177889736, (1, 5) = .0, (2, 1) = .345717339320025, (2, 2) = .11748530886258848, (2, 3) = -.44685722355458307, (2, 4) = -.42619398711861173, (2, 5) = .2456380242084213, (3, 1) = .3295368928873986, (3, 2) = -.10281256306809654, (3, 3) = -0.9786766510705683e-1, (3, 4) = -.22929557876687195, (3, 5) = .1827710770439118, (4, 1) = .2211740580910692, (4, 2) = -.12239573074044155, (4, 3) = 0.26569430715397205e-1, (4, 4) = -.10715356554772232, (4, 5) = 0.9622754869041322e-1, (5, 1) = .1264140268653532, (5, 2) = -0.8591949919337281e-1, (5, 3) = 0.4505713786209132e-1, (5, 4) = -0.4672290447819592e-1, (5, 5) = 0.44058134414995835e-1, (6, 1) = 0.6583176447988233e-1, (6, 2) = -0.4973034058218495e-1, (6, 3) = 0.332224698170035e-1, (6, 4) = -0.1969778835995821e-1, (6, 5) = 0.18945794068761176e-1, (7, 1) = 0.32315267535371534e-1, (7, 2) = -0.2600272586003493e-1, (7, 3) = 0.19495025439737884e-1, (7, 4) = -0.8174310046940966e-2, (7, 5) = 0.792388079531917e-2, (8, 1) = 0.15247583407686798e-1, (8, 2) = -0.12786769213836738e-1, (8, 3) = 0.10247087352154351e-1, (8, 4) = -0.3368066407962972e-2, (8, 5) = 0.3274729438901535e-2, (9, 1) = 0.6998105041282296e-2, (9, 2) = -0.604035420324911e-2, (9, 3) = 0.5052618825463968e-2, (9, 4) = -0.13833280384499146e-2, (9, 5) = 0.13465343117974211e-2, (10, 1) = 0.31478225677167735e-2, (10, 2) = -0.2774978205981712e-2, (10, 3) = 0.2390999068816236e-2, (10, 4) = -0.5673463700191876e-3, (10, 5) = 0.5524949194085244e-3, (11, 1) = 0.13945650673762352e-2, (11, 2) = -0.12492766558546968e-2, (11, 3) = 0.1099873594304329e-2, (11, 4) = -0.23253747538797784e-3, (11, 5) = 0.22648713664049123e-3, (12, 1) = 0.6105700389362067e-3, (12, 2) = -0.553893319523471e-3, (12, 3) = 0.495675152838582e-3, (12, 4) = -0.9528435644133216e-4, (12, 5) = 0.9281083066054085e-4, (13, 1) = 0.26480452107368317e-3, (13, 2) = -0.24268469519682714e-3, (13, 3) = 0.21995944221136622e-3, (13, 4) = -0.39040038537364915e-4, (13, 5) = 0.3802744922108661e-4, (14, 1) = 0.11394909512081752e-3, (14, 2) = -0.10532867430154103e-3, (14, 3) = 0.9644275586103112e-4, (14, 4) = -0.15995006093854115e-4, (14, 5) = 0.15580272849724842e-4, (15, 1) = 0.4870000930855666e-4, (15, 2) = -0.45361559105776056e-4, (15, 3) = 0.41882130392897214e-4, (15, 4) = -0.655308793716169e-5, (15, 5) = 0.6383193495979208e-5, (16, 1) = 0.20679444144369147e-4, (16, 2) = -0.1941000219193855e-4, (16, 3) = 0.18046766192933517e-4, (16, 4) = -0.26847296756546684e-5, (16, 5) = 0.26151287212238395e-5, (17, 1) = 0.8718850547396554e-5, (17, 2) = -0.8259728398401262e-5, (17, 3) = 0.7726423999999988e-5, (17, 4) = -0.10999141617991744e-5, (17, 5) = 0.1071399573515949e-5, (18, 1) = 0.3640252978905283e-5, (18, 2) = -0.3497402269851553e-5, (18, 3) = 0.32902284142233035e-5, (18, 4) = -0.45063567228372506e-6, (18, 5) = 0.43895327171989055e-6, (19, 1) = 0.14944389063713663e-5, (19, 2) = -0.14735566530371413e-5, (19, 3) = 0.13947933808207162e-5, (19, 4) = -0.1846330205946365e-6, (19, 5) = 0.1798465459323782e-6, (20, 1) = 0.5925773918561377e-6, (20, 2) = -0.6170979188394264e-6, (20, 3) = 0.5889965143819995e-6, (20, 4) = -0.756490724910656e-7, (20, 5) = 0.7368792426442866e-7, (21, 1) = 0.2162423610813038e-6, (21, 2) = -0.25593520469778174e-6, (21, 3) = 0.24786242887731095e-6, (21, 4) = -0.3099182802156362e-7, (21, 5) = 0.3018838597520553e-7, (22, 1) = 0.6124869999887661e-7, (22, 2) = -0.10415162185182523e-6, (22, 3) = 0.10401001373336376e-6, (22, 4) = -0.12697548109268844e-7, (22, 5) = 0.12368372462174604e-7, (23, 1) = .0, (23, 2) = -0.414339042389871e-7, (23, 3) = 0.4439573249525663e-7, (23, 4) = -0.5307519484383215e-8, (23, 5) = 0.5169925441711597e-8}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(23, {(1) = .0, (2) = .8799831042532784, (3) = 1.763772371553262, (4) = 2.654402578229091, (5) = 3.553045082129558, (6) = 4.4586129408519, (7) = 5.368912785498599, (8) = 6.281998076176939, (9) = 7.196599390092052, (10) = 8.112001132142932, (11) = 9.027808856750797, (12) = 9.943796151122035, (13) = 10.859842591432589, (14) = 11.775909928091433, (15) = 12.69200195250145, (16) = 13.608108476818263, (17) = 14.524205241796912, (18) = 15.440280945947823, (19) = 16.356315458558022, (20) = 17.272324219157973, (21) = 18.18845135779876, (22) = 19.104508127436276, (23) = 20.0}, datatype = float[8], order = C_order); Y := Matrix(23, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.18677723346185155e-6, (1, 4) = .0, (1, 5) = -0.1601034189830942e-6, (2, 1) = 0.37448226506023734e-7, (2, 2) = -0.4882419193663561e-8, (2, 3) = 0.32590922758163096e-7, (2, 4) = 0.8384642286135039e-8, (2, 5) = -0.3822989163192259e-7, (3, 1) = 0.4178076522983118e-7, (3, 2) = -0.32454728940560626e-7, (3, 3) = 0.5559818911848743e-7, (3, 4) = 0.255368475385125e-7, (3, 5) = -0.26372934101735208e-7, (4, 1) = -0.3503349256133378e-8, (4, 2) = 0.23271413239470415e-7, (4, 3) = -0.13109277388977377e-7, (4, 4) = 0.1940395871477904e-7, (4, 5) = -0.21150015818914884e-7, (5, 1) = 0.9049822894255894e-8, (5, 2) = 0.2044098278596014e-7, (5, 3) = -0.23457165838090578e-7, (5, 4) = 0.2721022646410278e-8, (5, 5) = -0.3786091636826618e-8, (6, 1) = 0.27051273759362853e-7, (6, 2) = 0.15343716259627215e-9, (6, 3) = -0.21958032487259045e-8, (6, 4) = -0.4159511453386257e-9, (6, 5) = 0.38101170586747216e-10, (7, 1) = 0.29235514018364573e-7, (7, 2) = -0.453106337656716e-8, (7, 3) = 0.46319249349793395e-8, (7, 4) = 0.46342814231151797e-9, (7, 5) = -0.6792806203548744e-9, (8, 1) = 0.26054556255110013e-7, (8, 2) = -0.1882133375224601e-8, (8, 3) = 0.2244789452496081e-8, (8, 4) = 0.711835820669783e-9, (8, 5) = -0.8568477954792043e-9, (9, 1) = 0.24106962716022037e-7, (9, 2) = 0.1629685214904445e-9, (9, 3) = -0.11146494499834733e-9, (9, 4) = 0.45110688737061194e-9, (9, 5) = -0.539236754168219e-9, (10, 1) = 0.2374177391716608e-7, (10, 2) = 0.5860236135721297e-9, (10, 3) = -0.7196114662102999e-9, (10, 4) = 0.18313053413689276e-9, (10, 5) = -0.23112721605478909e-9, (11, 1) = 0.23938814887888642e-7, (11, 2) = 0.34670384490097316e-9, (11, 3) = -0.499387007098935e-9, (11, 4) = 0.40264060755003194e-10, (11, 5) = -0.6396528893681144e-10, (12, 1) = 0.2413280997412847e-7, (12, 2) = 0.8123434213412095e-10, (12, 3) = -0.18766851557521373e-9, (12, 4) = -0.10028889791867737e-10, (12, 5) = -0.5607571181840299e-12, (13, 1) = 0.24205166580449604e-7, (13, 2) = -0.4873554507228097e-10, (13, 3) = -0.9122645013749574e-11, (13, 4) = -0.1774384229814944e-10, (13, 5) = 0.13554216810388484e-10, (14, 1) = 0.24197923253315855e-7, (14, 2) = -0.7644103795235015e-10, (14, 3) = 0.5059366630228127e-10, (14, 4) = -0.12500071087031085e-10, (14, 5) = 0.11123935740845305e-10, (15, 1) = 0.24164459411748233e-7, (15, 2) = -0.6066740320325875e-10, (15, 3) = 0.5144731921398412e-10, (15, 4) = -0.63139041944452e-11, (15, 5) = 0.6018851574113935e-11, (16, 1) = 0.24133003199149926e-7, (16, 2) = -0.36959226456229056e-10, (16, 3) = 0.34807094444056334e-10, (16, 4) = -0.2296584459403134e-11, (16, 5) = 0.2328976704823776e-11, (17, 1) = 0.24111780059612412e-7, (17, 2) = -0.1873228504203057e-10, (17, 3) = 0.18878272014729034e-10, (17, 4) = -0.33241174545583766e-12, (17, 5) = 0.40568885552430346e-12, (18, 1) = 0.24099883385166445e-7, (18, 2) = -0.7930627600316472e-11, (18, 3) = 0.8419004595137473e-11, (18, 4) = 0.3767477185747604e-12, (18, 5) = -0.34832143812623605e-12, (19, 1) = 0.2409407001294113e-7, (19, 2) = -0.26201105239283355e-11, (19, 3) = 0.2849865664815142e-11, (19, 4) = 0.485146485573298e-12, (19, 5) = -0.5118521121703797e-12, (20, 1) = 0.24091528694372805e-7, (20, 2) = -0.4820658103323563e-12, (20, 3) = 0.3930534221642779e-12, (20, 4) = 0.37341039360175125e-12, (20, 5) = -0.4432984456493013e-12, (21, 1) = 0.24090485353105713e-7, (21, 2) = 0.12932248130697764e-12, (21, 3) = -0.4349598146471398e-12, (21, 4) = 0.22003866786553054e-12, (21, 5) = -0.31866839336921104e-12, (22, 1) = 0.24090016159892753e-7, (22, 2) = 0.14345040328921917e-12, (22, 3) = -0.5483809312163577e-12, (22, 4) = 0.9076616249531766e-13, (22, 5) = -0.20691039898422648e-12, (23, 1) = 0.24089729356345837e-7, (23, 2) = .0, (23, 3) = -0.4163274954165759e-12, (23, 4) = .0, (23, 5) = -0.12614313243075443e-12}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 23, [g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 5, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[23] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(1.8677723346185155e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(23, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(1..6, {(1) = 18446884187980970662, (2) = 18446884187980970838, (3) = 18446884187980971014, (4) = 18446884187980971190, (5) = 18446884187980971366, (6) = 18446884187980971542}), (3) = [y, g(y), diff(g(y), y), diff(diff(g(y), y), y), h(y), diff(h(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `D(h)` := pointto(data[2][6]); return ('`D(h)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc]

sol3 := dsolve([eval(sys_ode, n = 10), ics], numeric, output = operator, continuation = lambda)