Two-Dimensional Differential Equations

Abstract

In the previous chapter we studied differential equations in which quantities increased or decreased in a monotonic fashion, reaching a fixed point as time increased. We know that in the real world quantities can also oscillate up and down in a regular or irregular fashion. The one-dimensional differential equations in the previous chapter, which have a single variable and a first derivative, cannot produce oscillation. In this chapter we consider differential equations with either a pair of variables and their first derivatives, or a single variable and its first and second derivatives. These two classes of problems are equivalent and are called second-order or two-dimensional ordinary differential equations.