Write your differential equation :
Now change the indices so that you get in the series :
Now make the starting indice be the same for the two series :
You want this to be equal to x.
Make appear the factors of x.
By identification, we get :
Solve for the recursive relation :P
Note that if n is odd, then the coefficient of the power series is 0, since a1=0.
I've already made a big part of the working, so now it's you to go ! Good luck