anonymous
  • anonymous
What is the meaning of an exact differential equation?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
http://en.wikipedia.org/wiki/Exact_differential_equation
anonymous
  • anonymous
No Dude, wikipedia is giving some mathematical relations. It's meaning is not clear
LollyLau
  • LollyLau
LOL nice going. Wikipedia only shows complicated equations.

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anonymous
  • anonymous
Oh ok, I don't know about differential equations, so I thought I'd post a link.
anonymous
  • anonymous
here is a short nice definition http://www.youtube.com/watch?v=bwASJWS8ltM
LollyLau
  • LollyLau
http://en.wikipedia.org/wiki/Inexact_differential I believe the picture is a gag.
anonymous
  • anonymous
It's not enough. Why we are using the word EXACT to that differential equation??? What is the physical meaning of that??
LollyLau
  • LollyLau
physical meanings...
anonymous
  • anonymous
it's linked to functions of more than one variable. Ok. Let \[D \subset \mathbb{R}^2\] be a simply connected open domain on which the functions \[I : \mathbb{R}^2 \longrightarrow \mathbb{R}\] and \[J : \mathbb{R}^2 \longrightarrow \mathbb{R}\] are continuous. The implicit first order ODE of the form: \[I(x,y)dx + J(x,y)dy = 0\] is exact if there \[\textbf{exists}\] a function \[F : [I : \mathbb{R}^2 \longrightarrow \mathbb{R}\] with the property that \[\frac{\partial }{\partial x}F(x,y) = I(x,y)\] and \[\frac{\partial }{\partial y}F(x,y) = J(x,y).\] so the definition relies on the existence of such a function F.
anonymous
  • anonymous
sorry \[ F : \mathbb{R}^2 \longrightarrow \mathbb{R}\]

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