Editing Mathematical analysis (section)

=== Differential equations ===
{{Main|Differential equation}}
A differential equation is a [[mathematics|mathematical]] [[equation]] for an unknown [[function (mathematics)|function]] of one or several [[Variable (mathematics)|variables]] that relates the values of the function itself and its [[derivative]]s of various [[Derivative#Higher derivatives|orders]].<ref>{{cite book|first = Edward L.|last =  Ince|title =Ordinary Differential Equations|publisher =  Dover Publications|date = 1956|isbn=978-0486603490|url = https://books.google.com/books?id=mbyqAAAAQBAJ}}</ref><ref>[[Witold Hurewicz]], ''Lectures on Ordinary Differential Equations'', Dover Publications, {{isbn|0486495108}}</ref><ref name="Evans_1998"/> Differential equations play a prominent role in [[engineering]], [[physics]], [[economics]], [[biology]], and other disciplines.

Differential equations arise in many areas of science and technology, specifically whenever a [[Deterministic system (mathematics)|deterministic]] relation involving some continuously varying quantities (modeled by functions) and their rates of change in space or time (expressed as derivatives) is known or postulated. This is illustrated in [[classical mechanics]], where the motion of a body is described by its position and velocity as the time value varies. [[Newton's laws of motion|Newton's laws]] allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an [[equations of motion|equation of motion]]) may be solved explicitly.