A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself to its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines.

Differential equations take a form similar to:

where

The "order" of a differential equation depends on the derivative of the highest order in the equation. The "degree" of a differential equation, similarly, is determined by the highest exponent on any variables involved. For example, the differential equation shown in is of second-order, third-degree, and the one above is of first-order, first-degree.

## Example

Take the following differential equation:

Solving this equation shows that

A complete solution contains the same number of arbitrary constants as the order of the original equation. (This is because, in order to solve a differential equation of the