What is Differential equation?
[[File:Airflow-Obstructed-Duct.png|thumb|360px|A picture of airflow, modeled using a differential equation.]] A '''differential equation''' is a [[Mathematics|mathematical]] [[equation]] that involves [[variable]]s like <math>x</math> or <math>y</math>, 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 (mathematics)|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. ==Types of differential equations== If a differential equation only involves <math>x</math> and its [[Derivative (mathematics)|derivative]], the rate at which <math>x</math> changes, then it is called a first order differential equation. A higher-order differential equation has derivatives of other derivatives. If there are more variables than just <math>x</math> and <math>y</math>, then it is said to be a [[partial differential equation]]. Sometimes, something will obey several differential equations at the same time. These are said to be modeled by coupled differential equations. Some differential equations can be solved exactly, and some cannot. Sometimes one can only be estimated, and a [[computer program]] can do this very fast. Although they may seem overly-complicated to someone who has not studied differential equations before, the people who use differential equations tell us that they would not be able to figure important things out without them. Most [[scientist]]s and [[engineers]] (as well as [[mathematician]]s) take at least one [[Class (education)|course]] in differential equations while in college. Some mathematicians devote their career to investigating differential equations that are difficult to solve.