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calculate integral...

torabi 85 Maple 2018
integration
October 30 2018
1 3

hi.

I can not gain answer for integral.

Best

int.mw
 

restart

PDE := (12*kappa^2*psi^2*(-upsilon^2+1)*((3*Pi^2*Q^2*(nu*psi^2+1)/(32*(-nu^2+1))+Q^2*(Pi^2*cos(2*Pi*y)/(8*psi^2)+psi^2*cos(2*Pi*x)*Pi^2*cos(2*Pi*y)/(4*(psi^2+1)^2)+Pi^2*cos(4*Pi*y)/(32*psi^2)+psi^2*cos(2*Pi*x)*Pi^2*cos(4*Pi*y)/(2*(4*psi^2+1)^2)+psi^2*cos(4*Pi*x)*Pi^2*cos(2*Pi*y)/(8*(psi^2+4)^2)))*(2*Q*Pi^2*sin(Pi*x)^2*cos(Pi*y)^2-2*Q*cos(Pi*x)^2*cos(Pi*y)^2*Pi^2)+(2*Q*cos(Pi*x)^2*Pi^2*sin(Pi*y)^2-2*Q*cos(Pi*x)^2*cos(Pi*y)^2*Pi^2)*(3*Pi^2*Q^2*(psi^2+nu)/(32*(-nu^2+1))+Q^2*((1/8)*psi^2*cos(2*Pi*x)*Pi^2+psi^2*cos(2*Pi*x)*Pi^2*cos(2*Pi*y)/(4*(psi^2+1)^2)+(1/32)*psi^2*cos(4*Pi*x)*Pi^2+psi^2*cos(2*Pi*x)*Pi^2*cos(4*Pi*y)/(8*(4*psi^2+1)^2)+psi^2*cos(4*Pi*x)*Pi^2*cos(2*Pi*y)/(2*(psi^2+4)^2)))-8*Q^3*cos(Pi*x)*cos(Pi*y)*Pi^2*sin(Pi*x)*sin(Pi*y)*(-psi^2*Pi^2*sin(2*Pi*x)*sin(2*Pi*y)/(4*(psi^2+1)^2)-psi^2*Pi^2*sin(2*Pi*x)*sin(4*Pi*y)/(4*(4*psi^2+1)^2)-psi^2*Pi^2*sin(4*Pi*x)*sin(2*Pi*y)/(4*(psi^2+4)^2)))+beta*V^2/(1-Q*cos(Pi*x)^2*cos(Pi*y)^2)^2-8*Q*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2+8*Q*Pi^4*sin(Pi*x)^2*cos(Pi*y)^2-2*psi^2*(4*Q*Pi^4*sin(Pi*x)^2*sin(Pi*y)^2-4*Q*Pi^4*sin(Pi*x)^2*cos(Pi*y)^2-4*Q*cos(Pi*x)^2*Pi^4*sin(Pi*y)^2+4*Q*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2)-psi^4*(-8*Q*cos(Pi*x)^2*Pi^4*sin(Pi*y)^2+8*Q*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2))*(1-Q*cos(Pi*x)^2*cos(Pi*y)^2)^2*cos(Pi*x)^2*cos(Pi*y)^2

int(int(PDE, y = -1/2 .. 1/2), x = -1/2 .. 1/2)


 

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simplify an equation ...

torabi 85 Maple 2018
simplification
October 28 2018
0 1

hi.

According to the fhgure attaceh how i can gain the equation (2-27) . I write the equation (2-26) in maple but I couldnot to gain that result.

If possible to reach equation via maple?

Thanks

diff.mw
 

restart

FC := (1/2)*W_m^2*(c1*x^2+c2*y^2)+(E.(h^2))*W_m^2*(sum(An*((sinh(n*Pi/lambda)+n*Pi*cosh(n*Pi/lambda)/lambda)*cosh(2*n*Pi*y/a)-2*n*Pi*y*sinh(n*Pi/lambda)*sinh(2*n*Pi*y/a)/a)*cos(2*n*Pi*x/a)/(n^2*(sinh(n*Pi/lambda)*cosh(n*Pi/lambda)+n*Pi/lambda))+Bn*((sinh(n*Pi*lambda)+n*Pi*lambda*cosh(n*Pi*lambda))*cosh(2*n*Pi*x/b)-2*n*Pi*x*sinh(n*Pi*lambda)*sinh(2*n*Pi*x/b)/b)*cos(2*n*Pi*y/b)/(lambda^2*n^2*(sinh(n*Pi*lambda)*cosh(n*Pi*lambda)+n*Pi*lambda)), n = 1 .. n))

Warning,  computation interrupted

  

S := diff(FC, x); SS := diff(S, x)

g := subs(x = (1/2)*a, SS)

0

 (1)

coeff(g, sinh(n*Pi/lambda))

0

 (2)

``


 

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pdsolve does not work...

torabi 85 Maple 2018
differential-equation pde pdsolve
October 18 2018
0 2

why pdsolve does not work?

Q and alpha are constant. I want to find f(x,y).

Thanks
 

"restart: w(x,y) :=Q*sin^(2)(Pi*x)*sin^(2)(Pi*y)"

proc (x, y) options operator, arrow, function_assign; Q*sin(Pi*x)^2*sin(Pi*y)^2 end proc

 (1)

PDE := diff(f(x, y), x, x, x, x)+2*(diff(f(x, y), x, x, y, y))/alpha^2+(diff(f(x, y), y, y, y, y))/alpha^4+((diff(w(x, y), y, y))*(diff(w(x, y), x, x))-(diff(w(x, y), x, y))^2)/alpha^2

diff(diff(diff(diff(f(x, y), x), x), x), x)+2*(diff(diff(diff(diff(f(x, y), x), x), y), y))/alpha^2+(diff(diff(diff(diff(f(x, y), y), y), y), y))/alpha^4+((2*Q*sin(Pi*x)^2*Pi^2*cos(Pi*y)^2-2*Q*sin(Pi*x)^2*sin(Pi*y)^2*Pi^2)*(2*Q*Pi^2*cos(Pi*x)^2*sin(Pi*y)^2-2*Q*sin(Pi*x)^2*sin(Pi*y)^2*Pi^2)-16*Q^2*sin(Pi*x)^2*sin(Pi*y)^2*Pi^4*cos(Pi*x)^2*cos(Pi*y)^2)/alpha^2

 (2)

pdsolve(PDE)

``


 

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plot for differential equation in time d...

torabi 85 Maple 2018
differential-equation plotting
October 16 2018
1 9

Hi.

How I can Plot voltage (v) versus time (t) in nonlinear differential equation.

if possible please provide a simple example for me. for instance the command that I must use!!

plot.pdf

non-trial solution...

torabi 85 Maple 2018
dsolve numeric differential-equations
September 28 2018
1 8

how I can find an non-trial solution (non-zero) for differential equations?

Thanks

y.mw
 

> 

restart; Nb := 2; Nt := .5; f1 := Nb*(diff(sigma(y), y, y))+Nt*(diff(theta(y), y, y)) = 0; f2 := diff(theta(y), y, y)+Nb*(diff(sigma(y), y))*(diff(theta(y), y))+Nt*(diff(theta(y), y))^2 = 0; f3 := (D(sigma))(0) = 0; f4 := (D(theta))(0) = 0; f5 := sigma(1) = 0; f6 := theta(1) = 0; f7 := dsolve({f1, f2, f3, f4, f5, f6}, {sigma(y), theta(y)}, numeric, output = listprocedure); plots:-odeplot(f7, [[y, sigma(y)]], y = 0 .. 1, legend = [y], labels = [y, sigma(y)]); plots:-odeplot(f7, [[y, theta(y)]], y = 0 .. 1, legend = [y], labels = [y, theta(y)])

2

  

.5

  

2*(diff(diff(sigma(y), y), y))+.5*(diff(diff(theta(y), y), y)) = 0

  

diff(diff(theta(y), y), y)+2*(diff(sigma(y), y))*(diff(theta(y), y))+.5*(diff(theta(y), y))^2 = 0

  

(D(sigma))(0) = 0

  

(D(theta))(0) = 0

  

sigma(1) = 0

  

theta(1) = 0

  

[y = proc (y) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); YP := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = -.0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = -.0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = -.0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = -.0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = -.0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = -.0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = -.0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 8, [sigma(y), diff(sigma(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[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[sigma(y), diff(sigma(y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 4)] 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[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 4, 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(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(1..5, {(1) = 18446746401092086174, (2) = 18446746401092086614, (3) = 18446746401092086790, (4) = 18446746401092086966, (5) = 18446746401092087142}), (3) = [y, sigma(y), diff(sigma(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, sigma(y) = proc (y) local res, data, solnproc, `sigma(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(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); YP := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = -.0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = -.0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = -.0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = -.0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = -.0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = -.0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = -.0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 8, [sigma(y), diff(sigma(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[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[sigma(y), diff(sigma(y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 4)] 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[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 4, 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(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(1..5, {(1) = 18446746401092086174, (2) = 18446746401092086614, (3) = 18446746401092086790, (4) = 18446746401092086966, (5) = 18446746401092087142}), (3) = [y, sigma(y), diff(sigma(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 `sigma(y)` := pointto(data[2][2]); return ('`sigma(y)`')(y) end if end if; try res := solnproc(outpoint); res[2] catch: error end try end proc, diff(sigma(y), y) = proc (y) local res, data, solnproc, `diff(sigma(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(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); YP := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = -.0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = -.0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = -.0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = -.0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = -.0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = -.0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = -.0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 8, [sigma(y), diff(sigma(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[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[sigma(y), diff(sigma(y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 4)] 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[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 4, 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(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(1..5, {(1) = 18446746401092086174, (2) = 18446746401092086614, (3) = 18446746401092086790, (4) = 18446746401092086966, (5) = 18446746401092087142}), (3) = [y, sigma(y), diff(sigma(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(sigma(y),y)` := pointto(data[2][3]); return ('`diff(sigma(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[3] catch: error end try end proc, theta(y) = 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(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); YP := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = -.0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = -.0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = -.0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = -.0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = -.0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = -.0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = -.0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 8, [sigma(y), diff(sigma(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[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[sigma(y), diff(sigma(y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 4)] 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[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 4, 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(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(1..5, {(1) = 18446746401092086174, (2) = 18446746401092086614, (3) = 18446746401092086790, (4) = 18446746401092086966, (5) = 18446746401092087142}), (3) = [y, sigma(y), diff(sigma(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][4]); return ('`theta(y)`')(y) end if end if; try res := solnproc(outpoint); res[4] catch: error end try end proc, diff(theta(y), y) = proc (y) local res, data, solnproc, `diff(theta(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(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); YP := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = -.0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = -.0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = -.0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = -.0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = -.0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = -.0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = -.0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(8, {(1) = .0, (2) = .1428571428571428, (3) = .2857142857142856, (4) = .4285714285714285, (5) = .5714285714285715, (6) = .7142857142857144, (7) = .8571428571428572, (8) = 1.0}, datatype = float[8], order = C_order); Y := Matrix(8, 4, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 8, [sigma(y), diff(sigma(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[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(8, 4, X, Y, outpoint, yout, L, V) end if; [y = outpoint, seq('[sigma(y), diff(sigma(y), y), theta(y), diff(theta(y), y)]'[i] = yout[i], i = 1 .. 4)] 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[8] elif outpoint = "order" then return 2 elif outpoint = "error" then return HFloat(-0.0) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 8, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[8] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[8] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false) ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(8, 4, 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(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(8, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(1..5, {(1) = 18446746401092086174, (2) = 18446746401092086614, (3) = 18446746401092086790, (4) = 18446746401092086966, (5) = 18446746401092087142}), (3) = [y, sigma(y), diff(sigma(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(theta(y),y)` := pointto(data[2][5]); return ('`diff(theta(y),y)`')(y) end if end if; try res := solnproc(outpoint); res[5] catch: error end try end proc]

  

 

 
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