Finding initial value of differential equation Given,
$$ mdv/dt = mg - kv $$
Question is:  

Find the velocity $v(t)$ that satisfies this initial value problem.
  Also, by letting $t$ approach positive infinity, determine the terminal velocity of the ball.

I first separated the equation and got
$$ dv/dt = g - k/mv $$
I have no clue how to approach this question. Can someone please help?

then terminal velocity is the constant velocity $v_\infty$ which is given by $$kv_\infty = m \, g \to v_\infty = \frac{mg} v.$$ we can now write the differential equation as $$\frac{dv }{dt} = \frac k m(v_\infty - v) \to \frac{dv}{v_\infty - v} = \frac k mdt$$ and can ve integrated to yield $$\ln(v_\infty - v) = -\frac k mt + \ln C \to v = v_\infty - Ce^{-kt/m}$$
