# MacLaurin Series solution to initial value problem

1. Mar 24, 2009

### tracedinair

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

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.

2. Relevant equations

3. 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 akxk?

2. Mar 25, 2009

### Staff: Mentor

I would go with the latter.