A differential equation is a mathematical relationship which contains one or more derivatives of a function. The solution of the differential equation is the original function. These equations are often used in scientific applications, particularly in physics and engineering, because they express rates of change in quantities of interest such as position, temperature, and other physical parameters. They also can be considered an extension of the basic study of calculus.

Differential equations are classified by several features. The order of a differential equation is given by the largest number of derivatives of a function featured in that equation - thus, an equation featuring third-derivatives of a function would be a third-order differential equation, but an equation featuring both third- and fourth-derivatives would be a fourth-order differential equation. Most differential equations used in practical applications are first- or second-order differential equations, as there are very few third-order...