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anonymous

  • 5 years ago

What is the meaning of an exact differential equation?

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  1. anonymous
    • 5 years ago
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    http://en.wikipedia.org/wiki/Exact_differential_equation

  2. anonymous
    • 5 years ago
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    No Dude, wikipedia is giving some mathematical relations. It's meaning is not clear

  3. LollyLau
    • 5 years ago
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    LOL nice going. Wikipedia only shows complicated equations.

  4. anonymous
    • 5 years ago
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    Oh ok, I don't know about differential equations, so I thought I'd post a link.

  5. anonymous
    • 5 years ago
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    here is a short nice definition http://www.youtube.com/watch?v=bwASJWS8ltM

  6. LollyLau
    • 5 years ago
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    http://en.wikipedia.org/wiki/Inexact_differential I believe the picture is a gag.

  7. anonymous
    • 5 years ago
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    It's not enough. Why we are using the word EXACT to that differential equation??? What is the physical meaning of that??

  8. LollyLau
    • 5 years ago
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    physical meanings...

  9. anonymous
    • 5 years ago
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    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.

  10. anonymous
    • 5 years ago
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    sorry \[ F : \mathbb{R}^2 \longrightarrow \mathbb{R}\]

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