Differential equation

mathematical equation involving derivatives of an unknown function

A differential equation is a mathematical equation that involves variables like or , 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.

A picture of airflow, modeled using a differential equation.

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 change

If a differential equation only involves   and its derivative, the rate at which   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   and  , 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 scientists and engineers (as well as mathematicians) take at least one course in differential equations while in college. Some mathematicians devote their career to investigating differential equations that are difficult to solve.

Uses change

Differential equations are used in many fields of science since they describe real-world things:

People who studied about differential equations change

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