I am trying to solve this equation using the series $\sum_0^\infty a_nx^n$
y'' - xy'+(3x-2)y=0
How to do that? I mean that I can replace the variables using the series but then I cannot add this thing cause the limits of the sums are not the same. Maybe I am doing something wrong here. I tried to make all sums start from $0$ with $x^{n+1}%$. This will leave $2a_2 - 2a_0 + \sum\dots = 0$ and I don't know what to do. I can't just say that $2a_2 = 2a_0 = 0$ cause it may be $2a_2 - 2a_0 = 0$. Well I am really confused.