# Homework Help: Series Solution around singular point

1. Jan 22, 2012

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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?

2. Jan 23, 2012

### vela

Staff Emeritus
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?

Last edited: Jan 23, 2012