# Nonlinear diff equation and power series

1. Nov 11, 2012

### Helpeme

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

i need to solve this diff equation.

y' = x2 + y2

y = 1 when x = 0

i can assume that the answer is a power series on the form Ʃanxn

andi only need the 4 first non zero terms of the power-series answer

2. Relevant equations

Ʃanxn

3. The attempt at a solution

y = Ʃanxn
y' = Ʃnanx(n-1)

Ʃn*anx(n-1) - (Ʃanxn)2 = x2

i guess since the answer is only 4 first non zero term. i can write out the summation to 4 terms.

if i do that im stuck with a bunch of a1 a2 a3 .... and i cant mange to find the value of those coefficients. and i dont really know if that is the right way of doing it at all.