# Solve a differential equation using series expansions.

Given an ODE such as $$y''+x^2y'+y=0$$ Is it possible to get sage to display the solution in the from (at least the first few terms of the expansion) $$y=a_o\left(c_0+c_1x+c_2x^2+\dots\right) + a_1\left(d_0+d_1x+d_2x^2+\dots\right) $$

EDIT: I have made some progress, functional but it is not pretty. second attempt