I have a differential equations problem that I thought someone here may be able to help with. So here goes:
In the motion of an object through a certain medium (air at certain pressures is an example), the medium furnishes a resisting force proportional to the square of the velocity of the moving object. Suppose a body falls due to the action of gravity, through the medium. Let t represent time, and v represent velocity, positive downward. Let g be the usual constant acceleration of gravity, and let w be the weight of the body. Use newton's law, for equals mass times acceleration, to conclude that the differential equation of motion is
where kv^2 is the magnitude of the resisting force furnished by the medium.