Second order ODE (mupad)

What's wrong??? How can i run this basic program?

% Solve 2nd order ODE
clc;clear all;

syms  y(x) k

eq='(1-x^2)*D2y - 2*x*Dy +(1+k)*k*y=0';

ic='y(0)=0, Dy(0)=1';    % Initial conditions

y=dsolve(eq, ic,'x')

k=2;

y=subs(y)

Messages :(R2014a)

Error using mupadmex

Error in MuPAD command: The first argument must not be negative. [orthpoly::legendre]

Error in sym/subs>mupadsubs (line 139)

G = mupadmex('symobj::fullsubs',F.s,X2,Y2);

Error in sym/subs (line 124)

G = mupadsubs(F,X,Y);

Error in dsolve_legendre1 (line 10)

y=subs(y)

Answer 1

[Birdman]

syms y(x)
k=2;
eq=(1-x^2)*diff(y,x,2)-2*x*diff(y,x)+(1+k)*k*y==0;
Dy=diff(y,x);
ic=[y(0)==0,Dy(0)==1];
y=dsolve(eq,ic,x)

I did this for command line, not MuPaD.

[Sibel]

thanks for your help

Answer 2

[Walter Roberson]

In R2014a, if you dsolve() with symbolic k then the solution that you get for y is

-orthpoly::legendre(- ((2*k + 1)^2)^(1/2)/2 - 1/2, x)*int(1/((y^2 - 1)*orthpoly::legendre(- ((2*k + 1)^2)^(1/2)/2 - 1/2, y)^2), y, 0, x)*orthpoly::legendre(- ((2*k + 1)^2)^(1/2)/2 - 1/2, 0)

Here, orthpoly::legendre is a reference to an MuPAD routine to calculate legendre polynomials.

Unfortunately when you subs in any real-valued k in that expression, the first argument to orthpoly::legendre becomes negative, and MuPAD does not like to compute that, leading to the error you see.

cvklpstunc showed computing with a specific numeric k: that works where using symbolic k and substituting in later does not.

This is a limitation in the R2014a symbolic engine. It is overcome in some later version.