# Eigenvalue problem; second order differential equation.

I have arrived at following differential equation

$$\psi^{''} + (x^2 - E/x + E^2) \psi =0$$, where $$E$$ is a constant.

Is it possible to recast this equation as an eigenvalue problem, that is:

$$\psi^{''} + f(x) \psi = a (E) \psi.$$

• Is this from physics? Is $E$ energy? Quite curious about the context. As for the question itself, obviously you can't recast this in the form you want for the same function $\psi$, you'll need to change the function and/or the variable, and even in that case I'm not sure. Possibly, you'll have to solve the problem iteratively – Yuriy S Nov 10 '18 at 12:47