Differential equation Hermite polynomials

[dakold]

I got a problem in quantum physics that i have come to a differential equation but I don't see how to solve it, its on the form
F''(x)+(Cx^2+D)F(x)=0.
How should I solve it?
Thanks

 

[dextercioby]

Isn't this the ODE for the Hermite polynomials ?

 

[dakold]

yes it's. i tried to make a ansatz with hermite polynomials and it solved the equation.