Maybe you can help me with this ODE question? It says to use the method of variation of parameters to find the general solution to

y'' + xy' + y = xe^(-x^2/2) given that one solution is e^(-x^2/2) and the other is that sum of series.

The only way I know how to do this is by solving for two functions v1' and v2' but the series is throwing me off.

If you have any ideas that would be great.