Mechanics Problem

Hi all
This is my first post and I'm fairly certain it will not be my last. I recently went back studying mathematics after a couple of decades in the wilderness and I'm really struggling to get my head around it. Here's my problem:

A particle of mass m moves along a horizontal x-axis. For all speeds greater than it's initial velocity the driving force is inversely proportional to it's speed and it's resistance to motion is proportional to the square of it's speed.

Right, I'm supposed to derive this equation of motion, if x is the distance travelled:

(m.v)dv/dx = (F.u)/v - (k.v^2) (v = vel, u = initial vel, F = magnitude of driving force and k = constant)

Could someone please point me in the right direction... ahmm, this is the first part of a 5 part question, i'm in serious trouble (Worried)

failing that.. could someone recommend a good book on this stuff.. i also have to do a nigh impossible question on hooke's law and another on kinetic and potential energy