It is often the case that the frictional force on an object will increase as the object moves faster. A fortunate example of this is the parachutist; the role of the parachute is to produce a frictional force due to air drag, which is larger than would normally be the case without the parachute. Consider a very simple example in which the frictional force depends on the velocity. Assume the object velocity obeys an equation of the form {dv}/{dt}= a - bv where a and b are constants. Think of as coming from a force applied such a gravity and b from friction or drag $(b > 0)$. Required:
Solve this equation exactly and using the euler method and compare both solutions.