Nonlinear first-order differrential equation

[keize1]

Homework Statement

m*dv/dt = - mg - kv^2, where m,g and k are constants and v(t) is what I should solve

Homework Equations

The Attempt at a Solution

At first I solved homogeneous equation m*dv_h/dt = -kv_h^2 and got v_h = m/(kt - cm). Where c is also constant.
Then I treid to get one solution for the original inhomogeneous equation by subtituting v = f(t)*v_h = f(t)*m/(kt - cm) in the original equation, but by it I only got a more difficult differential equation for f(t). So it didn't work.

I also tried a few different subtitutions at the beginning with no success.

 

[LawrenceC]

You could separate the variables such as:

dy/dx = f(y)

integral (dy/f(y)) = integral(dx)

Initial condition determines integration constant.