Systems of Differential Equations

We have focused our attention on solving ordinary differential equations that involve one dependent variable. However, many physical situations are modeled with more than one differential equation and involve more than independent variable. For example, if we want to determine the population of two interacting populations in a predator-prey relationship, such as foxes and rabbits, we have two dependent variables representing the two populations. In a basic model of the interaction of these two populations, these populations depend on one independent variable representing time. Situations similar to these lead to systems of differential equations.