# Thread: Show that the power series is the solution to the differential equation

1. ## Show that the power series is the solution to the differential equation

I know $y'=\sum_{n=0}^\infty \frac{(-1)^n(n+1)x^n}{n!(n+1)!}=\sum_{n=0}^\infty \frac{(-1)^nx^n}{(n!)^2}$
But I can't seem to simplify the rest or even know what to do when I do. I understand how to FIND the power series but I can't figure out how to go backwards.