Hello,

hence

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.

Hence :

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