# Homework Help: Radius of convergence question

1. Feb 22, 2009

### josh146

1. The problem statement, all variables and given/known data
What feature of the ODE explains your value for the radius of convergence of the series y2?
y2 is a series which satisfies the ODE and I found that it converges for $$\abs{2x^2} < 1$$.

2. Relevant equations
$$y2=x-\frac{2}{3}x^2-\frac{4}{15}x^5+ \cdots$$

ODE: $$(1-2x^2)\frac{d^2y}{dx^2} +4y = 0$$

3. The attempt at a solution
I presume this has something to do with the $$(1-2x^2)$$ in the ODE but I'm not sure. Can someone help?