1. The problem statement, all variables and given/known data I have to solve the differential equation xy'' + y' + xy = 0 ; x_o = 0 2. Relevant equations 3. The attempt at a solution I know that a solution is y= sum from 0 to infinity (an (x-1)^n) I then differentiate it twice to get y' = sum from 1 to inifinity (nan(x-1)^(n-1)) and y'' = sum from 2 to infinity (n(n+1)an(x-1)^(n-2)) then sub into the equation. Once It's in the equation I multiply y'' and y by (x-1) and add the correcting factor. Which would give me adding 5 series in total. Now, I just don't know how to add these series together. The n has to be same. And the exponent on (x-1) has to be the same as well. I'm not sure how to write this out so it looks nicer.