For the record, here is the problem from Marion and Thornton:
"As the simplest example of the resisted motion of a particle, find the
displacement and velocity of horizontal motion in a medium in which the
retarding force is proportional to the velocity.....the Newtonian equation
F=ma provides us with the equation of motion
ma = m (dv/dt) = -kmv where kmv is the magnitude of the resisting force (k
equals constant) ...."