Series solutions for differential equation

[ktklam9]

Homework Statement

Use the power series to solve the following differential equations, state the first four terms of the two independent solutions.

3xy'' + y' - y = 0

Homework Equations

The power series.

The Attempt at a Solution

How do I get two independent solutions out of this? All of my coefficients will depend on the first a...?

 

[Dick]

Your differential equation is singular at x=0. There are two solutions but one of them is singular at x=0. Your power series solution will only pick up the nonsingular one.

 

[ktklam9]

Ah ok, so the problem is screwed up from the beginning, thanks :)

 

[hedipaldi]

Search for the form of the series solution near a regular singular point.