View source for Differential equation

==English==
{{wikipedia}}

===Etymology===
First appears c. 1704 in the publications of {{w|Charles Hayes (mathematician)|Charles Hayes}}. {{calque|en|la|aequatio differentialis}}, which was coined by {{w|Leibniz}} in 1676.

===Pronunciation===
* {{audio|en|LL-Q1860 (eng)-Flame, not lame-differential equation.wav|a=US}}

===Noun===
{{en-noun}}
{{examples|examples=<math>\frac{dP}{dt}=kP+1000</math>}}

# {{lb|en|calculus}} An [[equation]] involving the [[derivative]]s of a [[function]].

====Derived terms====
{{col|en
|DE
|delay differential equation
|diff EQ
|{{l|en|ordinary differential equation}} ([[ODE]])
|{{l|en|partial differential equation}} ([[PDE]])
|stochastic differential equation
}}

====Translations====
{{trans-top|equation involving the derivatives of a function}}
* Catalan: {{t|ca|equació diferencial|f}}
* Chinese:
*: Mandarin: {{t+|cmn|微分方程|tr=wéifēn fāngchéng}}, {{t+|cmn|微分方程式|tr=wéifēn fāngchéngshì}}
* Czech: {{t|cs|diferenciální rovnice|f}}
* Danish: {{t|da|differentialligning|c}}
* Dutch: {{t+|nl|differentiaalvergelijking}}
* Esperanto: {{t|eo|diferenciala ekvacio}}
* Finnish: {{t+|fi|differentiaaliyhtälö}}
* French: {{t+|fr|équation différentielle|f}}
* German: {{t+|de|Differentialgleichung|f}}
* Hungarian: {{t+|hu|differenciálegyenlet}}
* Italian: {{t|it|equazione differenziale|f}}
* Japanese: {{t+|ja|微分方程式|tr=bibun hōteishiki|sc=Jpan}}
* Latin: {{t|la|aequātiō differentiālis|f}}
* Macedonian: {{t|mk|диференција́лна ра́венка|f}}
* Norwegian:
*: Bokmål: {{t|no|differensialligning|f|m}}, {{t|no|differensiallikning|f|m}}
*: Nynorsk: {{t|nn|differensiallikning|f}}
* Polish: {{t|pl|równanie różniczkowe|n}}
* Portuguese: {{t|pt|equação diferencial|f}}
* Romanian: {{t+|ro|ecuație diferențială|f}}
* Russian: {{t|ru|дифференциа́льное уравне́ние|n}}
* Serbo-Croatian: {{t|sh|diferencijalna jednadžba|f}}, {{t|sh|диференцијална једнаџба|f}}
* Spanish: {{t+|es|ecuación diferencial|f}}
* Swedish: {{t+|sv|differentialekvation|c}}
* Tagalog: {{t|tl|tingiring tumbasan}}
* Thai: {{t|th|สมการเชิงอนุพันธ์}}
* Turkish: {{t+|tr|diferansiyel denklem}}
* Vietnamese: {{t|vi|phương trình vi phân}}
{{trans-bottom}}

{{C|en|Differential equations}}