[Differential equation at the end; All the intermediary stuff is the problem behind it.] I was curious about finding the velocity function for a free-falling object using solely newton's equations. Using the force diagram, I've deduced that m-mass g-gravitational constant f_net - net force A - cross-sectional area v - velocity f_net = mg-1/4Av^2 ma = mg - (Av^2)/4 a=g-(Av^2)/4m v'=g-(Av^2)/4m and g, A and m are constants. In this case, I simplified by assuming A=1, m=1 so the equation becomes the nonlinear first-order differential equation v'=9.8-.25v^2. How do you... solve this kind of equation?