# Solution to 2nd O.D.E. using power seris

1. Aug 2, 2004

### Jayzar_1

Can anyone show me a complete solution to the problem below using power series?

y"+xy=x^2 y(0)=1 , y'(0)=0

2. Aug 2, 2004

### Galileo

Start with assuming a solution in the form of a power series:
$$y=\sum_{n=0}^{\infty}a_nx^n$$

Plug it into your differential equation and simplify. I think you should get a recursive relation between your coefficients whose initial values $a_0$ and $a_1$ can be determined from your initial conditions.

Last edited: Aug 2, 2004
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