MHB How to solve an ODE in powers of x?

[ineedhelpnow]

I have this question due soon and I have no idea how to do it. Please help me get started on it

Solve in powers of x: (1-x^2)y''-2xy'+42y=0

 

[MarkFL]

Re: Solving in powers

The equation:

$$\left(1-x^2\right)y''-2xy'+n(n+1)y=0$$

where $n\in\mathbb{N}$ is called Legendre's differential equation which has as solutions:

Legendre polynomials

That should give you a place to start. :D

 

[ineedhelpnow]

Thank You, Mark! I'll try working on it and reply with any problems I have