Solve the ordinary differential equation $\frac{d^2}{dx^2}F(x)=\frac{1}{F(x)^2}$ I've been trying to solve the ordinary differential equation
$$\frac{d^2}{dx^2}F(x)=\frac{1}{F(x)^2}$$
I tried simplifying and then simplifying even further and found that this function has to be in the form $e^{-cx}$ where $c$ is expressed in terms of the function itself therefore it means its a recurring function...So I need to know a function(that is not recurring) that is inversley proportional to its second derivative.I've  been trying to solve this for a long time but couldn't find anything online that was much help either.Help would be appreciated. Thanx in advance

It is a VERY difficult equation. If you are just interested for a solution try this by Wolfram:

