Power series solutions to differential equations

[Kate2010]

Homework Statement

I'm revising at the moment and a bit stumped on question 4 http://www.maths.ox.ac.uk/system/files/attachments/AC104.pdf

Homework Equations

The Attempt at a Solution

I think for the first part of the question, the regular singular points are 0 and -2.

However, I am unsure as to how to tackle the next part. I have assumed it is ok to differentiate the power series term by term and have done so and subbed it back into the original equation, now I feel like I need to equate coefficients, but I feel like I have no idea what I'm doing. If you could point me in the right direction I'd be really grateful :).

 

[hunt_mat]

This is the method of Frobenius, there are examples everywhere on the net.

 

[Kate2010]

Thanks :) I get it now.