A friend and I are having troubles setting up our differential equation for a free fall. The problem says this:
A body of a mass "m" falls from a certain height with a velocity "v". During the fall, the force due to air resistance is proportional to the square of the speed. Find the equation that represents its movement.
I think the differential equation should look like this:
$$m \frac{dv}{dt} = -mg + kv^2$$
But he thinks it should look like this:
$$mx'' - (x')^2 = 0$$
Which just does not make sense to me, since I don't think it would be a second order differential equation.