Exact differential equation

In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering. == Definition == Given a simply connected and open subset D of R 2 {\displaystyle \mathbb {R} ^{2}} and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form I ( x , y ) d x + J ( x , y ) d y = 0 , {\displaystyle I(x,y)\,dx+J(x,y)\,dy=0,} is called an exact differential equation if there exists a continuously differentiable function F, called the potential function, so that ∂ F ∂ x = I {\displaystyle {\frac {\partial F}{\partial x}}=I} and ∂ F ∂ y = J .

Source: Wikipedia — Exact differential equation (CC BY-SA 4.0)