Math Help - eigenvalues of legendre's equation

1. eigenvalues of legendre's equation

$(1-x^2)y''-2xy+y \lambda =0$
Why $\lambda$ must be n(n+1) ?
This is the Sturm-Liouville problem that leads to Legendre Polinomials

2. Re: eigenvalues of legendre's equation

Can you give more context?

3. Re: eigenvalues of legendre's equation

What's the definition of Legendre polynomial you have to use here?