The linear differential operator
$$L=\frac{d^2}{dx^2}+2x{\frac{d}{dx}}+6 $$
is given, and then a differential equation $$Lf_1(x)=0$$ is given, where $$f_1(x)=e^{-x^2}g(x) $$ and it is assumed that $$g(x)=a+bx+x^2 $$ .I was wondering what I need to do in order to find one solution to the differential equation and a second solution $$f_2(x)$$ of L?