1. The problem statement, all variables and given/known data 2. Relevant equations All relevant equations are given above. 3. The attempt at a solution I decided to make a substitution for x2 so that x2 = u. By doing that, I could make the k=n+1 and k=n-1 substitutions so I can keep the series in phase. I took y' and just plugged everything into the DE. In the 2xy part, I just pulled the x into y so that I get the x2n+1 term. However, I can't seem to combine the series in one without having a loose term included (the first term of the y' series). I get the combined series with the loose term, all equal to zero - and I don't know where to go from there.