ABSTRACT
Systems of differential equations arise very naturally in many physical contexts. In general it is quite difficult to find both a particular solution and the general solution to the associated homogeneous equations for a given system. Imagine an island inhabited by foxes and rabbits. Foxes eat rabbits; rabbits, in turn, develop methods of evasion to avoid being eaten. The resulting interaction is a fascinating topic for study, and is amenable to differential equations. To appreciate the nature of the dynamic between the foxes and the rabbits, the chapter describes some of the vectors at play. When the foxes become too numerous and eat too many rabbits, then the rabbit population declines; as a result, the foxes enter a period of famine and their population begins to decline. As the foxes decrease in number, the rabbits become relatively safe and their population starts to increase again.
