Talk:Exact differential equation

dx and dy?

Guys, the very first formula in our definition contains these undefined and confusing dx and dy terms. Leibniz's notation is terribly confusing for precisely this reason! You can't just have them lying around in a formula like that! Maelin (Talk | Contribs) 16:28, 30 June 2010 (UTC)

That is the notation found in a great many standard works on ODE, e.g. Ordinary Differential Equations, E.L.Ince 1926 First page Chapter 2 Exact Equations of the First Order and First Degree. Jszigeti (talk) 18:35, 6 April 2018 (UTC)

R²

What does R² mean?--NoPetrol (talk) 03:12, 14 July 2010 (UTC)

"The notation Rⁿ refers to the Cartesian product of n copies of R". See notation at Real_number#Notation. AdamTReineke (talk) 10:31, 6 February 2013 (UTC)

Error in given solution?

The solution that is currently shown is not quite correct. One can check this by a simple differentiation. When we differentiate F with respect to x, we should get I(x,y). However, what we get with what is currently posted in the article is:

${\frac {\partial F}{\partial x}}={\frac {\partial }{\partial x}}\int _{x_{0}}^{x}I(t,y_{0})dt+{\frac {\partial }{\partial x}}\int _{y_{0}}^{y}J(x,t)dt$

While the first term is simply I(x,y), the second term is definitely not zero, due to the dependence on x.

Looking through the history, it appears that sometime in 2007, this part of the article was re-written, and a correction term got dropped due to what I guessing is a cut-and-paste error.

Mathguthrie (talk) 21:52, 7 October 2012 (UTC)

Exact Differential equations

It would be nice to see an actual real life use that apply to these equations. 2603:6011:F741:6B0D:E9C6:A6D7:67E8:DA4 (talk) 01:41, 31 March 2022 (UTC)

Note

This article should mention that exact differential equation solutions stick to constant lines of their potential function! It's important for understanding. Mrfoogles (talk) 02:55, 4 February 2026 (UTC)