Editing Differential equation (section)

===Ordinary differential equations===
{{main|Ordinary differential equation|Linear differential equation}}
An [[ordinary differential equation]] (''ODE'') is an equation containing an unknown [[function of a real variable|function of one real or complex variable]] {{mvar|x}}, its derivatives, and some given functions of {{mvar|x}}. The unknown function is generally represented by a [[variable (mathematics)|variable]] (often denoted {{mvar|y}}), which, therefore, ''depends'' on {{mvar|x}}. Thus {{mvar|x}} is often called the [[independent variable]] of the equation. The term "''ordinary''" is used in contrast with the term [[partial differential equation]], which may be with respect to ''more than'' one independent variable.

[[Linear differential equation]]s are the differential equations that are [[linear equation|linear]] in the unknown function and its derivatives. Their theory is well developed, and in many cases one may express their solutions in terms of [[antiderivative|integrals]].

Most ODEs that are encountered in [[physics]] are linear. Therefore, most [[special functions]] may be defined as solutions of linear differential equations (see [[Holonomic function]]).

As, in general, the solutions of a differential equation cannot be expressed by a [[closed-form expression]], [[numerical ordinary differential equations|numerical methods]] are commonly used for solving differential equations on a computer.