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i solve 4 ODE with boundary condition.. i try to plot a graph F(eta) with different value of M.. but it doesnt comeout.. anyone can help me please??

restart; with*plots; n := .2; B := .5; R := 2; N := 10

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+.5*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

(1)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;

G(eta)*(diff(F(eta), eta))+F(eta)^2+.5*F(eta)-.5*(diff(f(eta), eta)) = 0

(2)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

G(eta)*(diff(G(eta), eta))+.5*f(eta)+.5*G(eta) = 0

(3)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(4)

bcs1 := f(0) = R, (D(f))(0) = 1, (D(f))(N) = 0, F(N) = 0, G(N) = -f(N), H(N) = n;

f(0) = 2, (D(f))(0) = 1, (D(f))(10) = 0, F(10) = 0, G(10) = -f(10), H(10) = .2

(5)

L := [2, 3, 5];

[2, 3, 5]

(6)

for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, bcs1}, M = L[k]), [f(eta), F(eta), G(eta), H(eta)], numeric, output = listprocedure); Y || k := rhs(R[5]); YP || k := rhs(R[6]); YR || k := rhs(R[7]) end do:

odeplot(R, [eta, f(eta)], 0 .. 10);

odeplot([eta = proc (eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); _solnproc := _dat[1]; if member(eta, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(eta, `=`) and member(lhs(eta), ["initial", 'initial']) then if type(rhs(eta), 'list') then _res := _solnproc("initial" = [0, op(rhs(eta))]) else _res := _solnproc("initial" = [1, rhs(eta)]) end if; if type(_res, 'list') then return _res[1] end if elif eta = "sysvars" then return _dat[3] end if; eta end proc, f(eta) = proc (eta) local res, data, solnproc, `f(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (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(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `f(eta)` := pointto(data[2][2]); return ('`f(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[2] catch: error  end try end proc, diff(f(eta), eta) = proc (eta) local res, data, solnproc, `diff(f(eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (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(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(f(eta),eta)` := pointto(data[2][3]); return ('`diff(f(eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc, diff(diff(f(eta), eta), eta) = proc (eta) local res, data, solnproc, `diff(diff(f(eta),eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (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(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(diff(f(eta),eta),eta)` := pointto(data[2][4]); return ('`diff(diff(f(eta),eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[4] catch: error  end try end proc, F(eta) = proc (eta) local res, data, solnproc, `F(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (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(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `F(eta)` := pointto(data[2][5]); return ('`F(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc, G(eta) = proc (eta) local res, data, solnproc, `G(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (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(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `G(eta)` := pointto(data[2][6]); return ('`G(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc, H(eta) = proc (eta) local res, data, solnproc, `H(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, 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(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] 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[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] 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(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, 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(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (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(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `H(eta)` := pointto(data[2][7]); return ('`H(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[7] catch: error  end try end proc], [eta, f(eta)], 0 .. 10)

(7)

``

(8)

print([(Y || (1 .. 3))(0)]);

[HFloat(0.0662575289978352), HFloat(0.06239249313847126), HFloat(0.05664455547330386)]

(9)

print([(YP || (1 .. 3))(0)]);

[HFloat(-2.308757932969589), HFloat(-2.2878028202715557), HFloat(-2.2574484928181637)]

(10)

print([(YR || (1 .. 3))(0)]);

[HFloat(0.20000866382583435), HFloat(0.20000675928400788), HFloat(0.2000045400222304)]

(11)

odeplots([Y || (1 .. 1)], 0 .. 10, labels = [eta, F(eta)]):

``


Download hydro92.mw

Hello everyone!

I used Maple 17 to fit an ellipse to a set of points using the following guide:

http://www.maplesoft.com/applications/view.aspx?SID=1395&view=html

My rotated ellipse was calculated to be:

SOL;

0.3939708949 x^2 - 0.005975799853 + 0.6345432059 y^2

But everytime I try to graph it in Maple 17, it only shows the axes and nothing else. Any help would be extremely appreciated.

I am interested in using both in the same graph. And I am aware that i can drag from one to the other manually, but I am interesseted in doing it in a command. 

So i have 3 vectors a, b and an error. 

I can define ExponentialFit function based on a and b, and the plotting both observations, errors and the fitted function.

 

Per Kirkegaard

 

I want to graph y=x^2, x>=0. but i want the axis to go from -2..2 so that you can see the restriction.  How do I go about this?

 

I'm trying to create a small app for Maple Player to graph solids of revolution. When I run the app in the desktop version of Maple T.A it works, but when I move it into the Maple Player App it crashes. Any ideas?

How can I join the points on this graph to look like the second graph below.

Hi,

I tried to create a graph with two different x-axes and y-axes, for example:

It's no doubt that we can use the "dualaxisplot" to generated a plot with two different y-axes as follows:

 

 

It's seem that Maple can realize plots with two different x-axes , because some of cases present functions through upper x-axis, such as:

 

How should I create a graph to display functions using the bottom and left sides as the x- and y-axis for one, and the top and right sides as the x- and y-axis for the other?

I'd appreciate any help on this topic. Thank a lot.

 

Greetings to all.

This past year I have on occasion shared mathematical adventures with cycle index computations and Maple, e.g. at these links:

Befitting the season I am sending another post to continue this series of cycle index computations. I present two Maple implementations of Power Group Enumeration as described by Harary and Palmer in their book "Graphical Enumeration" and by Fripertinger in his paper "Enumeration in Musical Theory." It was a real joy working with Maple to implement the computational aspects of their work, i.e. the Power Group Enumeration Theorem. Moreover the resulting software is easy to read, simple and powerful and has a straightforward interface, taking advantage of many different capabilities present in Maple.

The problem I am treating is readily described. Consider a cube in 3 space and its symmetries under rotation, i.e. rigid motions. We ask in how many different ways we may color the edges of the cube with at most N colors where all colors are completely interchangable, i.e. have the symmetric group acting on them in addition to the edge permutation group of the cube. At the following Math Stackexchange Link  I have posted the Maple code to implement the algorithms / formulas of Harary / Palmer / Fripertinger to solve this problem. The reader is invited to study and test these algorithms. It seems to me an excellent instance of computational combinatorics fun.

To conclude I would like to point out that these algorithms might be candidates for a Polya Enumeration Theorem (PET) package that I have been suggesting for a future Maple release at the above posts, the algorithms being of remarkable simplicity while at the same time providing surprisingly sophisticated combinatorics and enumeration methods.

Season's greetings!

Marko Riedel

Hi, i am trying to export the following bifurcation diagram into a pdf.

 

Digits:=20: N:=10000: M:=100: x_max:=1: r_min:=0:
r_max:=4: for n from 0 to N do r:=r_min+n/N*(r_max-r_min):
x:=evalf(x_max*rand()/10^12):for m from 0 to M do x:=x*exp(r*(1 - x)): od:
X[n]:=x: od:
with(plots):
bifpoint:={seq([r_min+j/N*(r_max-r_min),X[j]],j=0..N)}:
pitchf:=pointplot(bifpoint,symbol=point):display(pitchf);

 

For some reason the graph is just blank, with just the axis when i export to pdf.

Hi, 

Apologies if this is a very simple question and I am being a bit stupid, but how do I plot two functions of r on one graph, if they operate over different values of r? 

Say I have the functions:

FOO = r→APOT*exp(-r/rho)-CPOT/r^6+4*E2/r 

g = r→(c1*exp(d1*r)+c2*exp(d2*r)+c3*exp(d3*r)+c4*exp(d4*r))/r 

where FOO takes values of r between 0.5 and 2, and g takes values of r between o.2 and 0.5. 

 

Any help would be appreicated!

I need to plot the band structure of Graphene using Maple, Ive written out the eqn as given in the homework, but when i hit enter it says "error. unable to match delimiters"

 

i have no idea what that means, here is the eqn i have typed into Maple:

http://imageshack.us/photo/my-images/39/j7ri.jpg/

http://img39.imageshack.us/img39/733/j7ri.jpg

i have been given values for gamma and acc, do i just type them in after, E is a function of k (kx,ky,kz) do i put that in brackets after the E?

 

E(kx,ky,kz)

I need help finding the 10th order power series and graphing it. The initial problem is x2y''+xy'+x2y=0 with initial conditions y(0)=0 and y'(0)=0. Whenever I try using dsolve({eqn, y(0) = 0, (D(y))(0) = 0}, y(x), type=series) where eqn= the initial problem, it doesn't give an output, not even an error message. And help or ideas at all would be greatly appreciated.

Dears 

I want to sum some series by Maple and plotting. The problem is the sum of series are known like

serer.pdf

the problem is the difference between two graphs at the intersection x-axis and y-axis.

Is there any solution for this problem.

Amr

I have to plot 4 vectors in one graph. I have the following structure:

plot(Vector([12, 12.5, 13, 13.5, 14, 14.5, 15]), Vector([1.622712644, 1.265443137, 1.028604736, .8605013333, .7352916667, .6386248233, .5618945274]), style = line, symbol = asterisk, color = blue)

and 

plot(Vector([12, 12.5, 13, 13.5, 14, 14.5, 15]), Vector([5.483608580, 4.289400489, 3.496793877, 2.933480578, 2.513320599, 2.188469637, 1.930230220]), style = line, symbol = asterisk, color = blue)

Could you help me to plot these two curves in one graph.

 

please help me to find a solution for this issue...

I would like to thank you in advance

Best regards,

D.L.

Hello All,

I have had a few questions that have come up while working on a Maple Assignment for my Calculus III class. I was wondering if anybody could help me with these questions, as well as show me how to enter them in Maple. Here are the questions I have been struggling with.

 

  1. In the xy-plane, graph the ellipse ((x-4)^2)/(4))+(y-4)^2=1 and two level curves of F(x,y)=x^3+y^3-3xy that just touch the ellipse.

                  a. What do we know about the gradients of F and the ellipse at those points?

                  b. Use your graph to approximate the minimum and maximum values of F subject to the constraint ((x-4)^2)/(4))+  (y-4)^2=1.

 

      2. A company manufactures a product using inputs x,y,z according to the production function Q(x,y,z)=20x^(1/2)y^(1/4)z^(2/5). The prices per unit are $7 for x, $12 for y, and $18 for z.

                 a. Create the cost function

                 b. The company wants to produce 2500 products. Estimate the minimum cost by using the graph of the level surfaces of the cost function (from part a) together with the production constraint.

Any help you could give me would be much appreciated. Thanks!!

 

 

            

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