Hi all,

While solving some physics problem I came across a differential equation.

$\displaystyle \frac{\mathrm{d}^2y}{\mathrm{d}x^2}+c_1x^2y=c_2y$

Where all the constants $\displaystyle c_1$ and $\displaystyle c_2$ are positive. I need a solution for this equation. Please indicate me how to go about this. It will be helpful if the solution is in closed form. It might be helpful to know that, the solution to,

$\displaystyle \frac{\mathrm{d}^2y}{\mathrm{d}x^2}-c_1x^2y=c_2y$

is a product of hermite polynomials with a Gaussian envelope.

Thanking you.

Shantanu.