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:

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

  • $\begingroup$ 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 $\endgroup$ – Yuriy S Nov 10 '18 at 12:47

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