solution to 2nd O.D.E. using power seris

[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

[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.