Not sure how this can be done. can anyone help?
Have you made an attempt?
If you don't know what the method of Frobenius is, then you should look it up. It usually comes under power series solutions of ODEs.
I tried, i know that y''P(x)y'+Q(x)y = 0.
P(x) = (1-x)^2
Q(x) = (n^2+n)
but im not sure what to do in terms of legendre polynomial.
The Legendre polynomials are the solutions to this type of ODE. For the moment, forget Legendre Polynomials.
What you must do is use the method of Frobenius to solve the given ODE. If you do it correctly, your solution should come out equal to the series expression given. Note: these solutions are series with a finite number of terms.
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