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Question: How do complicated substitution in ode?

Question:How do complicated substitution in ode?

salim-barzani 255 Maple 2024
ode differentiation substitution differential-equations coefficients duplicate-question
January 17 2025
1

i try to get same result by substituation but i don't know what is mistake after i take second derivative is wronge i don't know how get same result as in paper did can anyone help  to calculate this part is not hard but is complicated ,How calculated second derivative and put in our ode to get the parameters?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
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" with(Student[ODEs][Solve]):"
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_local(gamma)
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declare(Omega(x, y, t)); declare(U(xi)); declare(u(x, y, t)); declare(Q(xi)); declare(V(xi)); declare(W(xi)); declare(f(xi))

Omega(x, y, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

  

u(x, y, t)*`will now be displayed as`*u

  

Q(xi)*`will now be displayed as`*Q

  

V(xi)*`will now be displayed as`*V

  

W(xi)*`will now be displayed as`*W

  

f(xi)*`will now be displayed as`*f

 (2)
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NULL
> 

ode := -delta*(diff(diff(U(xi), xi), xi))+U(xi)*(w^2-gamma*U(xi)-beta-alpha) = 0

-delta*(diff(diff(U(xi), xi), xi))+U(xi)*(w^2-gamma*U(xi)-beta-alpha) = 0

 (3)
> 

ode1 := -delta*(diff(diff(f(xi), xi), xi))+f(xi)*(w^2-gamma*f(xi)-beta-alpha) = 0

-delta*(diff(diff(f(xi), xi), xi))+f(xi)*(w^2-gamma*f(xi)-beta-alpha) = 0

 (4)
> 

F := U(xi) = sum(tanh(xi)^(i-1)*(B[i]*sech(xi)+A[i]*tanh(xi)), i = 1 .. n)+A[0]

U(xi) = sum(tanh(xi)^(i-1)*(B[i]*sech(xi)+A[i]*tanh(xi)), i = 1 .. n)+A[0]

 (5)
> 

S := U(f(xi)) = sum(cos(f(xi))^(i-1)*(B[i]*sin(f(xi))+A[i]*cos(f(xi))), i = 1 .. n)+A[0]

U(f(xi)) = sum(cos(f(xi))^(i-1)*(B[i]*sin(f(xi))+A[i]*cos(f(xi))), i = 1 .. n)+A[0]

 (6)
> 

``
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n := 2

2

 (7)
> 

eval(ode1, S)

-delta*(diff(diff(f(xi), xi), xi))+f(xi)*(w^2-gamma*f(xi)-beta-alpha) = 0

 (8)

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