analytic solution to second-order nonlinear ordinary differential equation

Question

Is there any way to solve this equation analytically ?

$m\ddot{x} = B_0 \left( \frac{1}{x^4} - \frac{1}{(L-x)^4} \right)$

its supposed to describe this system

Answer 1

Hint.

$$ m \ddot x\dot x= B_0 \left( \frac{\dot x}{x^4} - \frac{\dot x}{(L-x)^4} \right) $$