In this problem I have a rocket that is accelerated from rest by thrust that varies with time according to: F=1000t, if 0<t<2.

I need to find velocity equation for the rocket if mass remains constant and the drag force is equal to ten times its velocity. Mass of the rocket is 1600 lb.

What I did so far:

m(dv/dt)=F-kv

After trying to separate variables I end up with:

dv + (kv/m)dt = (1000t/m)dt

As you can see I am not able to separate variables, and it does not look like diff. equation of the first order.

Can you help me?

Thank you.