Series Solution around singular point

[hadroneater]

Homework Statement

x(2 - x)y'' - (x - 1)y' + 2y = 0
Find the general solution in terms of a polynomial and a series in powers of x - 1.

Homework Equations

The Attempt at a Solution

Does the question basically ask for a series solution of the ODE at the regular point x = 1?
Then $y(x) = \sum^{∞}_{n = 0}c_{n}(x - 1)^{n}$
If I sub that into the ODE then I get a rather complicated algebraic mess for x(2 - x)y''. Is this the right way to solve this?

 

[vela]

Try changing variables from x to u=x-1. That'll simplify the algebra a bit.

I don't see how you're going to get a polynomial solution. Did you type the DE as given?