What is the proper way to do this problem as a power series? The way I'm doing it, I end up with a very complicated term.
how I'm doing it:
take the series for y and assume it's of the form series(from n =0 to inf) cn*(x^n)
derive it to get the y' power series. Then multiply the y series by x^2. From here, I try to do some index shifting but I think I'm doing it wrong because I reach a form that I can't do anything with.