1. The problem statement, all variables and given/known data So the question I've been asked is, that there is a moving car, at time t = 0, moving with a speed of 50 km/h. At t = 0, the car stops accelerating, and thereby slowing down due to two forces: The air resistance drag force A friction which is created by some magnets in the motor (description of this in section 2). Write a differential equation for the system, as a function of the cars decceleration. 2. Relevant equations The air resistance is given by: Fd = -(1/2)pCdAv2. Where p, Cd and A are constants The friction in this motor is given by: Fe = -k*v. Where k is a konstant. This is basicly just a description of a spring using Hooke's law. 3. The attempt at a solution Writing a differential equation for this systems seems fairly easy. All the forces that acts on the car is equal to Newton's 2nd law F = ma. The constants in the air resistance is given the letter C = -(1/2)pCdA. ma = C*v2-k*v Writing this as a differential equation gives: m (dv/dt) = C v2 - k v However solving it seems much more difficult. This is what I've come up with so far, but I simply just can't get on: k v + m (dv/dt) = C v2 (+ k v on both sides) (k v)/(c v2)+(m/(c v2)) dv = dt (divided by c v2 on both sides, and multiplied by dt). (k/c) (1/v) + (m/c) (1/v2) dv = dt (Rewriting the fractions). I the integrate both sides, where k/c and m/c are both constants, so I only focus on 1/v and 1/v2, which gives: (k/c) ln|v| + (m/c) ln|v2| = t + K (Where k is the constant.) Then I move both of the constants to they other side. ln|v| + ln|v2| = (t + k) (c/k) (c/m) then I take the exponential of both sides to get v. v + v2 = e(t+c)*(c2/(k m)) However this just seems completely wrong, because solving the remaining eqution for v just wont make sense. There must be an easier way to do this, but I can't figure it out.