MacLaurin Series solution to initial value problem

[tracedinair]

Homework Statement

Find the first six nonvanishing terms in the Maclaurin series solution of the initial value problem (x^2 - 3)y''(x) + 2xy'(x) = 0 where y(0) = y₀ and y'(0) = y₁.

Homework Equations

The Attempt at a Solution

Should with just something like Φ(x) such that Φ(x) = \sum from 0 to infinity of Φⁿ(x) / n! * xⁿ?

Or should I use the undetermined coefficient solution of the form \sum from k=0 to infinity of a_kx^k?

 

[Mark44]

I would go with the latter.