## anonymous 4 years ago What is the meaning of an exact differential equation?

1. anonymous
2. anonymous

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

3. LollyLau

LOL nice going. Wikipedia only shows complicated equations.

4. anonymous

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

5. anonymous

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

6. LollyLau

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

7. anonymous

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

8. LollyLau

physical meanings...

9. 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.

10. anonymous

sorry $F : \mathbb{R}^2 \longrightarrow \mathbb{R}$

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