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## Homework Statement

The task is to find an analytic solution to the O.D.E

[tex] 4(1-x^2)y''-y=0 \hspace{20mm} y'(1)=1[/tex]

by using an appropriate series solution about x=1.

## The Attempt at a Solution

The singularity at x=1 is regular, which makes me think the Frobenius method is what's meant by appropriate series solution. But I've always done these about x=0, so I suppose the form would be

[tex] y=\sum_{n=0}^{\infty} a_n (x-1)^{n+r} [/tex]

with

[tex] y''=\sum_{n=0}^{\infty} a_n(n+r)(n+r-1)(x-1)^{n+r-2} [/tex]

At this point I'd substitute into the O.D.E and find an indicial equation, but I'm not really sure how this works when we're expanding about x=1, or indeed if this is the right track. Any help or advice would be greatly appreciated!