Question

What is the meaning of an exact differential equation?

Answer 1

http://en.wikipedia.org/wiki/Exact_differential_equation

Answer 2

No Dude, wikipedia is giving some mathematical relations. It's meaning is not clear

Answer 3

LOL
nice going.
Wikipedia only shows complicated equations.

Answer 4

Oh ok, I don't know about differential equations, so I thought I'd post a link.

Answer 5

here is a short nice definition
http://www.youtube.com/watch?v=bwASJWS8ltM

Answer 6

http://en.wikipedia.org/wiki/Inexact_differential
I believe the picture is a gag.

Answer 7

It's not enough. Why we are using the word EXACT to that differential equation??? What is the physical meaning of that??

Answer 8

physical meanings...

Answer 9

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.

Answer 10

sorry \[ F : \mathbb{R}^2 \longrightarrow \mathbb{R}\]