Differential equation

A differential equation is a mathematical equation that involves variables like ${\displaystyle x}$ or ${\displaystyle y}$, as well as the rate at which those variables change. Differential equations are special because the solution of a differential equation is itself a function instead of a number.

In applications of mathematics, problems often arise in which the dependence of one parameter on another is unknown, but it is possible to write an expression for the rate of change of one parameter relative to another (derivative). In this case, the problem is reduced to finding a function by its derivative related to some other expressions.