A second order nonlinear ode in an electrostatics problem

[Judas503]

I encountered the following second order nonlinear ODE while solving a problem in electrostatics. The ODE is: \frac{d^{2}V}{dx^{2}} = CV^{-1/2}

How can I solve this?

Regards.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[TSny]

Normally, the Forum requires some attempt at a solution before help is given. In this case, either you have seen the trick or you haven't. So, I hope I'm not violating policy by going ahead and giving you a hint. Try multiplying both sides by 2 dV/dx.