Mechanics ODE Problem Particle

Question

I have a particle of mass $M$ which moves with a velocity $v$, such that;

$$Mv' = -Mg - kv^2$$ where $g$ and $k$ are positive, and its initial velocity is $U$, i.e $v(0) = U$.

I am then told that the particle travels until it becomes stationary, at a distance $D$ from it's original position.

I am looking for an expression for this distance, but I am unable to solve non linear second order ODEs so I am wondering if there is a different approach available?

Answer 1

This ODE is nonlinear, but first order (because there is only a first derivative to $t$). To solve it, use the method of separation of variables.