Actually a physics riddle, but won't quibble about that point. Having a B.S. in it myself, my curiosity was piqued, of course, went on a search to find what equation(s) he was working on and the solution he found, took forever but finally found it - link and 1st section of author's post below, keep reading to find the actual math/physics involved and proof that he did indeed solve the differential equations correctly in closed form:
The problem he solved is as follows:
Let (x(t),y(t)) be the position of a particle at time t. Let g be the acceleration due to gravity and c the constant of friction. Solve the differential equation:
(x''(t)2 + (y''(t)+g)2 )1/2 = c*(x'(t)2 + y'(t)2 )
subject to the constraint that (x''(t),y''(t)+g) is always opposite in direction to (x'(t),y'(t)).
Finding the general solution to this differential equation will find the general solution for the path of a particle which has drag proportional to the square of the velocity (and opposite in direction).
