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ahmadtalaei

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These are questions asked by ahmadtalaei

Solve a PDE with a known solution...

ahmadtalaei 25 Maple 16
substitution pdsolve operator
August 26 2020
2 3

Can anyone help me to find a solution to psi[2](r,phi) for the attached partial differential equation pde[0]?


I want to find a general solution to a partial differential equation by assuming that I know one solution, called psi[1], and trying to find another solution psi[2] by assuming that the general solution in the form of psi= psi[1]*psi[2]. I want to restrict the second solution to be in the form of psi[2](r*sin(phi)) so that it satisfies the PDE, and is a function of r times sin(phi). The latter makes error as the maple identifies that the function psi[2](r*sin(phi)) depends on only one variable r*sin(phi). Could you please help me to find a solution for psi[2] in the form psi[2]=f(r*sin(phi))?

 

Also, I have trouble with defining the operator Do in the attached file.  When it operates on psi[2](r * sin(phi)), maple gives D(D(psi[2]))(r*sin(phi)). It is not clear for me that whether this derivative is with respect to r or phi. I need is to define Do in a way so that the derivatives are correctly taken with respect to different separate variables.

 

Thank you for your help,

Ahmad

PDEs_KnownSolutoin.mw

Solve a system of partial differential e...

ahmadtalaei 25 Maple 16
pde pdsolve differential-equations
August 26 2020
1 2

Can anyone help me to solve the attached system of PDEs with a given expression for the HINT such as HINT = F[1](t)*F[2](r*sin(phi))

I am not able to set such an arbitray HINT function for system of PDEs.

SysPDE_HINT.mw

 

Thank you,

Ahmad

How to convert a function expressed by t...

ahmadtalaei 25 Maple 16
dsolve differential-equations legendre
June 07 2019
1 7

Anyone can help me to convert the following maple solution expressed by the hypergeom function to the LegendreP(n,b,x) or Q function?


 

> 

restart
> 

with(PDETools):
> 

infolevel[pdsolve] := 3:
> 

sol[1] := dsolve((1-x^2)*(diff(y(x), x, x))+n(n+1)*y(x) = 0)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

 (1)
> 

convert(sol[1], LegendreP)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

 (2)
> 

``

 

Download convert-Legendre.mw

 

https://math.stackexchange.com/questions/3254765/how-to-convert-a-hypergeom-function-to-the-legendre-function

I just want y(x) to be expressed in the form of LegendreP(n,b,x).

Maple: How to solve the given Partial Di...

ahmadtalaei 25 Maple 16
pde differential-equations duplicate-question
April 08 2019
1 5

I need help on solving the following PDE by Maple:

https://math.stackexchange.com/questions/3177491/how-to-solve-the-given-partial-differential-equation

I couldn't write the partial differential equation in Mapleprimes so provided the link from somewhere else. Please help. Thank you.

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