Solving an ODE Related to Relativistic Mass Change

[renlok]

Homework Statement

$$\frac{dp}{dt} = \frac{d}{dt}\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}} = F$$
Find v(t) show that v -> c as t -> infinity & find the distance traveled in time t if the object starts from rest.

Homework Equations

The Attempt at a Solution

Ive tried rearranging it into either a separable ODE or into the form ay'' + by' + cy = 0 but haven't gotten anywhere.

really grateful for any help :)

(I think i posted this in the wrong board...)

 

[fzero]

Is the force $$F$$ constant? If it is, this can be directly integrated from $$t=0$$ to $$t$$.