MaplePrimes Questions

First-timer,

How do I enter a double integral in Maple Learn? The bar has only single integrals. Using parenthesis yields dxdx. I can't use two separate integrals because the second intetral is Int(f(y)dx) not Int(f(y)dy).

Thanks

Mark

Here is my code:

 

t := 6*Pi; lambda := .1; N := 5; M := sqrt(N(N+1))*exp(I*phi); omegap := 1

eq1:=-2*(n(phi,delta)-N)+(u(phi,delta)-M)*exp(-2*I*omegap*t/lambda)+((z(phi,delta)-conjugate(M))*exp(2*I*omegap*t/lambda)):
eq2:=-2*(1-I*delta)*u(phi,delta)+2*(n(phi,delta)-N)*exp(2*I*omegap*t/lambda)+2*M:
eq3:=-2*(1+I*delta)*z(phi,delta)+2*(n(phi,delta)-N)*exp(-2*I*omegap*t/lambda)+2*conjugate(M):
convert(eq1, rational); convert(eq2, rational); convert(eq3, rational);

f1:=evalc(eq1);f1:=evalc(eq2):f3:=evalc(eq3)
f1 := solve{f1, f2, f3};
with(plots); Impliciplot3([n(phi,delta)], delta = -10 .. 10, phi = 0 .. 2*Pi);

 

Hi, 

I work with a parameterized ODE whose numerical solution is called sol.
The names of the parameters I get from sol(parameters) are not the same as the initial names I used.
I've been stuck on this problem for more almost two hours and I can't find out if I made a mistake or if it's a Maple problem.

Thanks for your help


 

restart

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

sys := { M__p * diff(x(t), t) = K*x(t), x(0) = 0};

{M__p*(diff(x(t), t)) = K*x(t), x(0) = 0}

(2)

params := [M__p, K];
sol    := dsolve(sys, numeric, parameters=params);

[M__p, K]

 

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := [M__p = M__p, K = K]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 24, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..54, {(1) = 1, (2) = 1, (3) = 0, (4) = 0, (5) = 2, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..3, {(1) = 0., (2) = Float(undefined), (3) = Float(undefined)})), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..1, {(1) = .1}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..1, {(1, 1) = .0}, datatype = float[8], order = C_order), Array(1..1, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = 0}, datatype = integer[8]), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8], order = C_order), Array(1..1, {(1) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..1, {(1, 1) = .0, (2, 0) = .0, (2, 1) = .0, (3, 0) = .0, (3, 1) = .0, (4, 0) = .0, (4, 1) = .0, (5, 0) = .0, (5, 1) = .0, (6, 0) = .0, (6, 1) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = x(t)]`; YP[1] := Y[3]*Y[1]/Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = x(t)]`; YP[1] := Y[3]*Y[1]/Y[2]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..3, {(1) = 0., (2) = 0., (3) = undefined}); _vmap := array( 1 .. 1, [( 1 ) = (1)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see <a href='http://www.maplesoft.com/support/help/search.aspx?term=dsolve,maxfun' target='_new'>?dsolve,maxfun</a> for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; _dat[4][26] := _EnvDSNumericSaveDigits; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, x(t)], (4) = [M__p = M__p, K = K]}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(3)

data := [params[1] = 10., params[2] = 10000.];

instance := sol(parameters=data);
whattype(%);

[M__p = 10., K = 10000.]

 

[M__p = 10., K = 10000.]

 

list

(4)

lprint(data); lprint(lhs~(data));

[M__p = 10., K = 10000.]

[M__p, K]

 

lprint(instance); lprint(lhs~(instance));

[M__p = 10., K = 10000.]

[M__p, K]

 

zip((u,v) -> evalb(u=v), lhs~(data), lhs~(instance))

[false, false]

(5)

zip((u,v) -> evalb(u=v), params, lhs~(instance))

[false, false]

(6)

zip((u,v) -> evalb(u=v), params, lhs~(data))

[true, true]

(7)

 


 

Download X_is_not_X.mw

 

Hello,

 

I have a problem with PDE coupled that I don't know how to solve in the maple.

Are there some analitical/numerical methods to solve the problem?

 

Any help will be usefull!!

 

 

I'm trying to find the interval of convergence for the sum

sum((x-2)^n/((x-2)^n),n=0..infinity)

```

c:=n-> 1/(n^2-1)
   c := proc (n) options operator, arrow; 1/(n^2-1) end proc

s:=x-> sum(c(n)*((x-2)^n), n=0..infinity)
 s := proc (x) options operator, arrow; sum(c(n)*x^n, n = 0 ..

    infinity) end proc


# figure out how to plot this, without making it crash
abs( (c(n+1)*x^(n+1)) / (c(n)*x^n) );
                      | (n + 1) / 2    \|
                      |x        \n  - 1/|
                      |-----------------|
                      |/       2    \  n|
                      |\(n + 1)  - 1/ x |

simplify( % );
                          |  / 2    \|
                          |x \n  - 1/|
                          |----------|
                          |n (2 + n) |

L:= limit( %, n=infinity );
                            L := |x|

solve( L<1, x );
                  RealRange(Open(-1), Open(1))

simplify( s(3) )
                            infinity

```

How do I get it to find the correct interval, which is [1,3] I get the correct radius, which is 1.

 

I'm able to export Maple documents as LaTeX, but I'm not able to execute them because I can't find the package in

{maplestd2e}

in MikTex.

How do I add this package to MikTex, and by extension, TexnicCenter?

For the Latex code of matrix B, I used the following procedure. But the last column of B is not what we're looking for in the latex code. (There is no problem in the other columns)

Download_Latexcode.mw

restart:
interface(rtablesize=20):
f:=(x,t)->x*t;
g:=(x,t)->x^2*t;
  
B:=Matrix([[x,t,"f(x,t)","g(x,t)"],
         seq(seq([i,j,f(i,j),g(i,j)],
                 j=0.125..0.875, 0.25),
             i=0.125..0.875,0.25)]):
B[1,..]:=map(p->nprintf(`#mi(%a);`,p),B[1,..]):
B[2..,4]:=map(p->nprintf(`#mn(\"%1.2e\");`,p),B[2..,4]):
 
 

Lat:=proc(M::Matrix,
          {output::{NoUserValue,identical(string)}:=':-NoUserValue'})
  local m,n,S;
  (m,n):=op(1,M);
  S:=cat(" \\begin{tabular}",
         "{|",seq("c|",i=1..op([1,2],M)),"} ",
         "\\hline ",
         seq([seq(sprintf("$%s$ & ",latex(M[i,j],':-output'=string)),j=1..n-1),
         sprintf("$%s$ \\\\ \\hline ",latex(M[i,n],':-output'=string))][],i=1..m),
         "\\end{tabular} ");
  if output=':-string' then
    return S;
  else
    printf("%s",S);
    return NULL;
  end if;
end proc:
Lat(B);

 

The input

f(x) := x^2;

n := evalf(int(f(x)^2, x = 0 .. 1));

f(x) :=  f(x)/n;

plot(f(x), x = 0 .. 1)

leads to the error

Error, (in f) too many levels of recursion
I need to reassign the function as itself divided by n that depends on the old f...

A piece of code like this is supposed to be inside a loop, so creating f_new(x):=f(x)/n doesn't solve the issue.

If it was a cpp code I'd write something like f(x)/=n for every x. How can I do it in Maple?

Thank you in advance for you answers!

with(plots, implicitplot);

eqn := (1 + ln(x))/x = 0;

plot1 := implicitplot(eqn, x = -10 .. 10, y = -10 .. 10)

 

I'm trying to plot this equation, however no lines are showing up on the graph at all. Am I doing something wrong?

The interval I set seems to be correct, double checked it in other software

Would like to export a list into a text file

when I tried , it show ... 1234 items... , can not export a whole list into text file.

[[[0,0,0,0]], [[0,0,0,0]], .....]
thousands of [[...]] elements

 

This is an issue I had for long time. Though to ask about it.

Any one who used Database[SQLite] in Maple probably know this.  I'd like to do kernelopts('assertlevel'=2): but this does not work when using Database[SQLite] as it raises assertion failed, due to the way data is read from database and converted to Maple variable.

It happens at the statement 

         variable_to_read := Database[SQLite]:-FetchAll(stmt); 

For an example, the table I have in sql, has many fields. some are strings and some are integers. Lets say I want to read field called run_it corresponding to rowid I enter. So I do this in Maple

local run_it::integer;
.....
counter :=1;

stmt := Database[SQLite]:-Prepare(conn, cat("SELECT run_it FROM PROBLEMS WHERE rowid=",convert(counter,string),";"));    

run_it := Database[SQLite]:-FetchAll(stmt); 

The assetion error happens at the second call above. 

Error, (in dsolver_test:-MAIN_STEP) assertion failed in assignment, expected integer, got Matrix(1, 1, {(1, 1) = 1}, order = C_order, attributes = [source_rtable = (Array(1..1, {(1) = 1}, order = C_order))]) 
 

Once I remove kernelopts('assertlevel'=2): everything works fine with no problems at all. So I been running my program for more than a year now without the assert set.

Since I have hundreds of  such calls, and I do not think try/catch will work here, any one knows of a way to handle this, so I can turn on assertlevel to help catch any other problems some where else in the program, and still use SQLite ?

I could make an example if needed. I would need to create new database file and so on. This will take time.

Maple 2020.2

ps. Database[SQLite] works very well and very fast. I am surprised how fast it reads the data. few thousands records, each is 25 fields, and it does it in few seconds. Good implementation.

Edit

I found that by removing all the type specification on my Maple variables, that I read the SQL data into using FetchAll(stmt);  it now works!

So I am able to now use kernelopts('assertlevel'=2):

So intead of doing  

local local run_it::integer;  and then call SQL, I just now do  local run_it; with no type.  I had to remove the type on many such variables I had.  Now no assertion error any more during the SQL calls.

This works for me for now. I should have done this long time ago, I just did not think about it before. I would have liked to keep the type here.

Edit: I see answer below that allows me to do this by changing assert level just for the call to SQL which is good solution.

 

 

 

 

In Maple 2020.2, and after I changed to interface(warnlevel=4); then once in a while, I now see this message 

                                  Warning, persistent store makes readlib obsolete

followed by name of the file and the line number. It always happen at calls to timelimit(the_time_limit,:-dsolve(....

It seems harmless so far, as I have not seen any side effect.

 

I googled and the above, and see few places where it shows up, but no clear explanation what it is and what it means. But the messages I saw at google are a little different. They look like this

               WARNING: persistent store makes one-argument readlib obsolete

While the one I get is a little different as you can see. (no one-argument in it)

I am using my own package in .mla file during running the code if this makes any difference.

Is there any place where it explains what this means and why it happens sometimes? Sorry, can't make MWE, since it seems to happen at random. But I noticed it always happens at call to dsolve when I saw it.

Maple 2020.2

Physics 884

Windows 10
 


 

[Preliminary analysis of the Question by Carl Love:

 

In the worksheet below, the OP numerically solves a BVP on an interval a..b, for several values of a parameter. Using the numeric solution procedures returned by dsolve, he wants to numerically integrate an algebraic expression (named P1 below) that uses several of the BVP's dependent variables as well as its independent variable. This integral is to be done on an interval c..d, where a < c < d < b (all inequalities strict). He's having trouble coming up with the correct syntax for this.

 

I (Carl) am confident that the dsolve calls are all syntactically correct and that they return solution procedures in the usual manner without raising any issues, numerical or otherwise. Whether the integrations will ultimately require some adjustments to dsolve's error-control options, I don't know at this point. This Question is only about syntax required to perform the integrations. Any error-control adjustments, if they're needed at all, will be handled later.

 

I (Carl) have only edited the the OP's worksheet to remove a large amount of content that is irrelevant to Answering this Question. I haven't changed any of the content; I've only deleted. Of course, I already have several ideas about what needs to be done, but up until this point I haven't acted as an Answerer but rather as a Moderator and Editor making this Question suitable for posting.

 

--Carl Love]

restart;

 

eq1:=diff(f(y), y$4)+Uhs*diff(E(y),y$3)-(diff(f(y), y$2))+(diff(theta(y), y$1))= 0:

eq2:=diff(theta(y), y$2)+(diff(f(y), y$2)+1)^2+1+diff(theta(y),y$2) = 0:

E:=y->zeta*(cosh(k/2*(h1+h2-2*y)))/(cosh(k/2*(h1-h2))):

bcs:=f(h1) = -(1/2)*(Q-1-d), f(h2) = (1/2)*(Q-1-d), (D(f))(h1) = -1, (D(f))(h2) = -1,theta(h1) = 0, theta(h2) = 1:

 

epsilon1:=0.1:d:=1:omega:=Pi/6:h1:=-(1+epsilon1*sin(2*Pi*x)):h2:=d+epsilon2*sin(2*Pi*x+omega):F:= Q-1-d:epsilon2:=0.5:x:=1:

alpha:=Pi/6:

de:=eq1,eq2,bcs:

d1 := subs(Uhs =-2, zeta=3,k=1,[de]):

param:= {Uhs =-2, zeta=3,k=1}:

P1:= eval(diff(f(y), y$3)+Uhs*diff(E(y),y$2)-(diff(f(y), y$1)+1)+(theta(y))+sin(alpha),param);

diff(diff(diff(f(y), y), y), y)-3.524364340*cosh(-.1250000000+y)-(diff(f(y), y))-1/2+theta(y)

(1)

ec:=0.5:

 

for Q from -3 to 3 by ec do
F2[Q]:=dsolve(d1, numeric,maxmesh=25500,continuation=lambda1,output=listprocedure):
P2[Q]:=subs(F2[Q],P1):  
end do:

for Q from -3 to 3 by ec do
P3[Q]:=evalf(Int(P2[Q],0..1));   
end do:

[Examination of any of the P2[Q] or P3[Q] will highlight the syntactic problem. --Carl]:

P2[-3];

proc (y) local res, data, solnproc, `diff(diff(diff(f(y),y),y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(diff(diff(f(y),y),y),y)` := pointto(data[2][5]); return ('`diff(diff(diff(f(y),y),y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc-3.524364340*cosh(-.1250000000+proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc)-proc (y) local res, data, solnproc, `diff(f(y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(f(y),y)` := pointto(data[2][3]); return ('`diff(f(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc-1/2+proc (y) local res, data, solnproc, `theta(y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `theta(y)` := pointto(data[2][6]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc

(2)

P3[-3];

Int(proc (y) local res, data, solnproc, `diff(diff(diff(f(y),y),y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(diff(diff(f(y),y),y),y)` := pointto(data[2][5]); return ('`diff(diff(diff(f(y),y),y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc-3.524364340*cosh(-.1250000000+proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); _solnproc := _dat[1]; if member(y, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(y, `=`) and member(lhs(y), ["initial", 'initial']) then if type(rhs(y), 'list') then _res := _solnproc("initial" = [0, op(rhs(y))]) else _res := _solnproc("initial" = [1, rhs(y)]) end if; if type(_res, 'list') then return _res[1] end if elif y = "sysvars" then return _dat[3] end if; y end proc)-1.*proc (y) local res, data, solnproc, `diff(f(y),y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `diff(f(y),y)` := pointto(data[2][3]); return ('`diff(f(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc-.5000000000+proc (y) local res, data, solnproc, `theta(y)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](y) else outpoint := evalf(y) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = 2.5, (1, 2) = -1.0, (1, 3) = -4.281464431036743, (1, 4) = 7.808769858127952, (1, 5) = .0, (1, 6) = 2.545581053812295, (2, 1) = 2.390895630449416, (2, 2) = -1.3622144303735313, (2, 3) = -3.6102389050468275, (2, 4) = 6.812427509247975, (2, 5) = .21228484191208993, (2, 6) = 2.100855515085262, (3, 1) = 2.2409516331509796, (3, 2) = -1.6850699622745682, (3, 3) = -2.9878715558503863, (3, 4) = 5.901852374747316, (3, 5) = .4020878367195957, (3, 6) = 1.7926862598309719, (4, 1) = 2.047458942025034, (4, 2) = -1.969304365813901, (4, 3) = -2.40990234447743, (4, 4) = 5.067299192463986, (4, 5) = .5796476057339995, (4, 6) = 1.5873338124681484, (5, 1) = 1.8058256387408347, (5, 2) = -2.215087360857704, (5, 3) = -1.8715584446083655, (5, 4) = 4.301392825136728, (5, 5) = .754184440029553, (5, 6) = 1.454343776166982, (6, 1) = 1.5080512702414115, (6, 2) = -2.4216216828372583, (6, 3) = -1.3668814159403284, (6, 4) = 3.5997272795214843, (6, 5) = .9343976409904876, (6, 6) = 1.364935846189515, (7, 1) = 1.1405996214689007, (7, 2) = -2.5855979232216675, (7, 3) = -.8882947678795358, (7, 4) = 2.9649111698520136, (7, 5) = 1.1286172660195575, (7, 6) = 1.2892745969584898, (8, 1) = .6980930912088831, (8, 2) = -2.695381423968232, (8, 3) = -.43980712463206023, (8, 4) = 2.4326930378698486, (8, 5) = 1.3365971730207493, (8, 6) = 1.19442542266601, (9, 1) = .1727860216657963, (9, 2) = -2.7376917267985372, (9, 3) = -0.11083192285675154e-1, (9, 4) = 2.0536756735478554, (9, 5) = 1.5529054938179532, (9, 6) = 1.0377373374133898, (10, 1) = -.3748833226717925, (10, 2) = -2.6998010311810097, (10, 3) = .3837338105778085, (10, 4) = 1.920836707496037, (10, 5) = 1.738529675497688, (10, 6) = .7940208131713947, (11, 1) = -.8798881347906011, (11, 2) = -2.591470262703322, (11, 3) = .7580885467182361, (11, 4) = 2.0544799214403433, (11, 5) = 1.8600354130540693, (11, 6) = .46331818617642156, (12, 1) = -1.2891943245931412, (12, 2) = -2.440041083880994, (12, 3) = 1.116082225065107, (12, 4) = 2.391513103167679, (12, 5) = 1.9055082022233873, (12, 6) = 0.780331992734655e-1, (13, 1) = -1.6163437890681935, (13, 2) = -2.260492303949706, (13, 3) = 1.4793584478256556, (13, 4) = 2.868958207476626, (13, 5) = 1.8874504307599422, (13, 6) = -.35723283962536084, (14, 1) = -1.8745187648570432, (14, 2) = -2.0624380594089535, (14, 3) = 1.8539841950195342, (14, 4) = 3.441971864194715, (14, 5) = 1.8172705496332988, (14, 6) = -.8397050434995353, (15, 1) = -2.082672450603434, (15, 2) = -1.8446048736475056, (15, 3) = 2.2538669497193315, (15, 4) = 4.103024375386881, (15, 5) = 1.6999673569244942, (15, 6) = -1.3876753194464726, (16, 1) = -2.2548610271364673, (16, 2) = -1.5979677934986705, (16, 3) = 2.700634162559218, (16, 4) = 4.875067631206399, (16, 5) = 1.5301977066644439, (16, 6) = -2.0396608494924555, (17, 1) = -2.393995878336207, (17, 2) = -1.3175379586363032, (17, 3) = 3.206029908379249, (17, 4) = 5.7730260911415705, (17, 5) = 1.2999779888786136, (17, 6) = -2.829389289599418, (18, 1) = -2.5, (18, 2) = -1.0, (18, 3) = 3.7779462768611785, (18, 4) = 6.8087698581275164, (18, 5) = 1.0, (18, 6) = -3.792478282731491}, datatype = float[8], order = C_order); YP := Matrix(18, 6, {(1, 1) = -1.0, (1, 2) = -4.281464431036743, (1, 3) = 7.808769858127952, (1, 4) = -11.682851906320586, (1, 5) = 2.545581053812295, (1, 6) = -5.884004406079647, (2, 1) = -1.3622144303735313, (2, 2) = -3.6102389050468275, (2, 3) = 6.812427509247975, (2, 4) = -10.034830150339626, (2, 5) = 2.100855515085262, (2, 6) = -3.9066735707100304, (3, 1) = -1.6850699622745682, (3, 2) = -2.9878715558503863, (3, 3) = 5.901852374747316, (3, 4) = -8.577101734799035, (3, 5) = 1.7926862598309719, (3, 6) = -2.475816661279518, (4, 1) = -1.969304365813901, (4, 2) = -2.40990234447743, (4, 3) = 5.067299192463986, (4, 4) = -7.266904719425421, (4, 5) = 1.5873338124681484, (4, 6) = -1.4939123104814767, (5, 1) = -2.215087360857704, (5, 2) = -1.8715584446083655, (5, 3) = 4.301392825136728, (5, 4) = -6.06220646584873, (5, 5) = 1.454343776166982, (5, 6) = -.8798070611840767, (6, 1) = -2.4216216828372583, (6, 2) = -1.3668814159403284, (6, 3) = 3.5997272795214843, (6, 4) = -4.917285662048078, (6, 5) = 1.364935846189515, (6, 6) = -.5673009866811901, (7, 1) = -2.5855979232216675, (7, 2) = -.8882947678795358, (7, 3) = 2.9649111698520136, (7, 4) = -3.7771053744479106, (7, 5) = 1.2892745969584898, (7, 6) = -.5062390294415434, (8, 1) = -2.695381423968232, (8, 2) = -.43980712463206023, (8, 3) = 2.4326930378698486, (8, 4) = -2.6060729675673855, (8, 5) = 1.19442542266601, (8, 6) = -.6569080288065, (9, 1) = -2.7376917267985372, (9, 2) = -0.11083192285675154e-1, (9, 3) = 2.0536756735478554, (9, 4) = -1.329244706880773, (9, 5) = 1.0377373374133898, (9, 6) = -.9889782262899456, (10, 1) = -2.6998010311810097, (10, 2) = .3837338105778085, (10, 3) = 1.920836707496037, (10, 4) = 0.18873581934085837e-1, (10, 5) = .7940208131713947, (10, 6) = -1.4573596292680913, (11, 1) = -2.591470262703322, (11, 2) = .7580885467182361, (11, 3) = 2.0544799214403433, (11, 4) = 1.4120260262718638, (11, 5) = .46331818617642156, (11, 6) = -2.0454376690509197, (12, 1) = -2.440041083880994, (12, 2) = 1.116082225065107, (12, 3) = 2.391513103167679, (12, 4) = 2.7730816513481105, (12, 5) = 0.780331992734655e-1, (12, 6) = -2.7389019916182473, (13, 1) = -2.260492303949706, (13, 2) = 1.4793584478256556, (13, 3) = 2.868958207476626, (13, 4) = 4.135987560886272, (13, 5) = -.35723283962536084, (13, 6) = -3.573609156402222, (14, 1) = -2.0624380594089535, (14, 2) = 1.8539841950195342, (14, 3) = 3.441971864194715, (14, 4) = 5.512415585971837, (14, 5) = -.8397050434995353, (14, 6) = -4.57261289271065, (15, 1) = -1.8446048736475056, (15, 2) = 2.2538669497193315, (15, 3) = 4.103024375386881, (15, 4) = 6.957126727084476, (15, 5) = -1.3876753194464726, (15, 6) = -5.793825063237893, (16, 1) = -1.5979677934986705, (16, 2) = 2.700634162559218, (16, 3) = 4.875067631206399, (16, 4) = 8.556222775957853, (16, 5) = -2.0396608494924555, (16, 6) = -7.347346602550183, (17, 1) = -1.3175379586363032, (17, 2) = 3.206029908379249, (17, 3) = 5.7730260911415705, (17, 4) = 10.363818056432482, (17, 5) = -2.829389289599418, (17, 6) = -9.345343795090377, (18, 1) = -1.0, (18, 2) = 3.7779462768611785, (18, 3) = 6.8087698581275164, (18, 4) = 12.426230981064215, (18, 5) = -3.792478282731491, (18, 6) = -11.914385312285798}, 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(18, {(1) = -1.0, (2) = -.908025825108771, (3) = -.809941624254285, (4) = -.7043389803571176, (5) = -.5891307667649807, (6) = -.4609863495490285, (7) = -.3145588746582628, (8) = -.14736901187051485, (9) = 0.4551641153657529e-1, (10) = .24647070233670992, (11) = .4369261674327891, (12) = .5993111123629165, (13) = .7382594709970882, (14) = .8574987237630365, (15) = .9638589421825318, (16) = 1.0636783801387402, (17) = 1.1588615165318914, (18) = 1.25}, datatype = float[8], order = C_order); Y := Matrix(18, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.11348329575773589e-8, (1, 4) = 0.4864701579333315e-8, (1, 5) = .0, (1, 6) = -0.10989585261420845e-7, (2, 1) = -0.35930797328257545e-9, (2, 2) = 0.1120726260246873e-8, (2, 3) = -0.3810334718083824e-9, (2, 4) = 0.10202310560003775e-7, (2, 5) = -0.42166476108451865e-8, (2, 6) = -0.5797553298898888e-8, (3, 1) = -0.597288569357346e-9, (3, 2) = 0.21222221068919605e-8, (3, 3) = -0.1137339463116378e-8, (3, 4) = 0.1438277391620926e-7, (3, 5) = -0.7395285212672763e-8, (3, 6) = -0.32173543335922633e-8, (4, 1) = -0.7193713816637941e-9, (4, 2) = 0.31382599442570602e-8, (4, 3) = -0.12104363333247733e-8, (4, 4) = 0.17865430868653026e-7, (4, 5) = -0.9861432635774536e-8, (4, 6) = -0.2493926860820792e-8, (5, 1) = -0.7178759115509634e-9, (5, 2) = 0.43672068941910126e-8, (5, 3) = -0.6217043986990342e-9, (5, 4) = 0.21092457235711023e-7, (5, 5) = -0.11858771389319843e-7, (5, 6) = -0.3210969909485222e-8, (6, 1) = -0.5687085103358607e-9, (6, 2) = 0.6170893992502247e-8, (6, 3) = 0.6626718989235696e-9, (6, 4) = 0.24593128415144597e-7, (6, 5) = -0.1355447471178518e-7, (6, 6) = -0.535916520461893e-8, (7, 1) = -0.2428278602175301e-9, (7, 2) = 0.929150558493132e-8, (7, 3) = 0.26930941402892048e-8, (7, 4) = 0.2910113448958189e-7, (7, 5) = -0.14939367425075547e-7, (7, 6) = -0.9660178501618373e-8, (8, 1) = 0.4684892476902608e-9, (8, 2) = 0.14156642089863336e-7, (8, 3) = 0.5787951696500473e-8, (8, 4) = 0.34600673847418134e-7, (8, 5) = -0.1556947279598061e-7, (8, 6) = -0.17306923664247353e-7, (9, 1) = 0.7682144916893278e-9, (9, 2) = 0.19817566959762203e-7, (9, 3) = 0.7685861346069001e-8, (9, 4) = 0.3860588296023259e-7, (9, 5) = -0.13908070911379652e-7, (9, 6) = -0.27740975604385757e-7, (10, 1) = 0.5287989918432325e-9, (10, 2) = 0.19324047908953415e-7, (10, 3) = 0.6320556842959638e-8, (10, 4) = 0.3530463270579722e-7, (10, 5) = -0.11101236233171745e-7, (10, 6) = -0.3082615480684206e-7, (11, 1) = -0.36083484861838476e-9, (11, 2) = 0.13383480245755086e-7, (11, 3) = 0.13731297163318004e-8, (11, 4) = 0.2675357757011373e-7, (11, 5) = -0.8497177362392062e-8, (11, 6) = -0.24096556062109797e-7, (12, 1) = -0.2684599190846042e-9, (12, 2) = 0.9189363753856766e-8, (12, 3) = -0.8016571917643014e-9, (12, 4) = 0.22287848803881498e-7, (12, 5) = -0.8229454268018357e-8, (12, 6) = -0.18809057626536594e-7, (13, 1) = 0.5391473589367901e-11, (13, 2) = 0.660112804540974e-8, (13, 3) = -0.15206872883977156e-8, (13, 4) = 0.1974531123930168e-7, (13, 5) = -0.827699705392898e-8, (13, 6) = -0.1522197676799441e-7, (14, 1) = 0.31082285582367075e-9, (14, 2) = 0.5082187127877483e-8, (14, 3) = -0.1379117710947162e-8, (14, 4) = 0.1833751871699261e-7, (14, 5) = -0.838895250919421e-8, (14, 6) = -0.1289342962895591e-7, (15, 1) = 0.5190240254053171e-9, (15, 2) = 0.39810838810844255e-8, (15, 3) = -0.11378619623679266e-8, (15, 4) = 0.1700122346111952e-7, (15, 5) = -0.8154191697451248e-8, (15, 6) = -0.10703162492646381e-7, (16, 1) = 0.5526177171660696e-9, (16, 2) = 0.2871340408929278e-8, (16, 3) = -0.13579309897192253e-8, (16, 4) = 0.1474584984894201e-7, (16, 5) = -0.70088864893549195e-8, (16, 6) = -0.7369877511141113e-8, (17, 1) = 0.386505556144586e-9, (17, 2) = 0.15846062546582246e-8, (17, 3) = -0.2326090607754289e-8, (17, 4) = 0.10928203588404684e-7, (17, 5) = -0.4478240228504296e-8, (17, 6) = -0.17137665357565461e-8, (18, 1) = .0, (18, 2) = .0, (18, 3) = -0.430549823112629e-8, (18, 4) = 0.4865136769215114e-8, (18, 5) = .0, (18, 6) = 0.7783493456211505e-8}, 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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 18, [f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] 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`(18, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(18, 6, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)]'[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[18] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(3.860588296023259e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 18, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[18] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[18] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (HFloat(7.0)), ( 2 ) = (HFloat(0.0)), ( 3 ) = (HFloat(0.0)), ( 4 ) = (HFloat(0.0)), ( 5 ) = (HFloat(0.0)), ( 6 ) = (HFloat(0.0))  ] ); L := Matrix(7, 2, {(1, 1) = 0.39124920294759724e-4, (1, 2) = 0.9524777402444147e-6, (2, 1) = 0.31072332469098585e-2, (2, 2) = 0.10401040644334418e-3, (3, 1) = 0.4668136080079607e-1, (3, 2) = 0.20533250078818475e-2, (4, 1) = .6915946911181323, (4, 2) = 0.21751110719627174e-1, (5, 1) = .2325899133886315, (5, 2) = -0.9632256764150957e-2, (6, 1) = 0.24955985049078054e-1, (6, 2) = -0.8159691734812938e-3, (7, 1) = 0.10316914761574886e-2, (7, 2) = -0.1850709262187998e-4}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = -2.1478336645470737, (2) = -1.7604123046776636, (3) = 2.4068158545390332, (4) = 4.364276134223538, (5) = 1.6459235084132278, (6) = -1.606109765425612}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(18, 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`(18, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446746772886867566, (2) = 18446746772886859862, (3) = 18446746772886860038, (4) = 18446746772886860214, (5) = 18446746772886860390, (6) = 18446746772886860566, (7) = 18446746772886860742}), (3) = [y, f(y), diff(f(y), y), diff(diff(f(y), y), y), diff(diff(diff(f(y), y), y), y), theta(y), diff(theta(y), y)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(y) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(y) else `theta(y)` := pointto(data[2][6]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc, 0. .. 1.)

(3)

 

``

Note: If I remove the cosh from P1 then everything works fine.

Download DP_sheet_0.1.mw

I'm trying to make a table of values as a data table.  The problem is that it's making more rows than loops, I'm not able to make an empty DataFrame, and that I have to add an extra row to align the values, so I need to remove a row, and change the indexes.  Any help with making data tables work properly, would be greatly appreciated.

```

newt := x -> evalf(x - f(x)/D(f)(x));

f:= x -> x^6-2; # function to analyze

rt[0] := 1.5; #x0 value


n_error[0]:=1.5-newt(1.5): #error of first estimate
     

DF := DataFrame( <x|n_error>):# create a dataframe to store estimates, and error rates
for count from 0 to 10 do; nerror[count]:=abs(x[count]-x[count-1]);    rt[count]:=x[count-1];
x[count + 1] := newt(x[count]); DF:=Append(DF,DataSeries(<rt[count]|nerror[count]>),mode=row);    
end do:

NewtonData:=DataFrame(Remove( DF, 2, mode=row)):
NewtonData


```

In the below paper 

ODEs are solved by using Matlab Software

Is it possible to solve this in Matlab software?  [I think you mean Maple!--Carl Love]

I have attached the Article

j.physa.2019.123959.pdf

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