# Solving a non-linear differential operator equation

Sorry if the title is misleading.

I am trying to obtain $V(r)$ from the following equation:

$\frac{\partial^2}{\partial t^2} C(r,t) = (-\frac{\partial^2}{\partial r^2} + V(r))^2 C(r,t)$

I can do this when $(-\frac{\partial^2}{\partial r^2} + V(r))$ is not squared but alas it is squared.

I am wondering if there are any neat ways of dealing with such equations. If I expand $(-\frac{\partial^2}{\partial r^2} + V(r))^2$ it doesn't get me anywhere. Have done some research but only helps me when $V(r)$ is a constant.

Any help would be appreciated.

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DE with two independent varables should be a PDE rather than an ODE. –  doraemonpaul Oct 12 '12 at 4:59