Editing Differential equation (section)

===Equation order and degree{{anchor|Second order|Order}}===
The '''order of the differential equation''' is the highest ''[[order of derivative]]'' of the unknown function that appears in the differential equation. 
For example, an equation containing only [[first-order derivative]]s is a ''[[first-order differential equation]]'', an equation containing the [[second-order derivative]] is a ''second-order differential equation'', and so on.<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>{{usurped|1=[https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation]}}, accessed Dec 2015.</ref>

When it is written as a [[polynomial equation]] in the unknown function and its derivatives, its '''degree of the differential equation''' is, depending on the context, the [[polynomial degree]] in the highest derivative of the unknown function,<ref>{{cite book |title=Elements of the Differential and Integral Calculus |author1=Elias Loomis |edition=revised |publisher=Harper & Bros. |year=1887 |isbn= |page=247 |url=https://books.google.com/books?id=DTI4AQAAMAAJ}} [https://books.google.com/books?id=DTI4AQAAMAAJ&pg=PA247 Extract of page 247]</ref> or its [[total degree]] in the unknown function and its derivatives. In particular, a [[linear differential equation]] has degree one for both meanings, but the non-linear differential equation <math>y'+y^2=0</math> is of degree one for the first meaning but not for the second one.

Differential equations that describe natural phenomena almost always have only first and second order derivatives in them, but there are some exceptions, such as the [[thin-film equation]], which is a fourth order partial differential equation.