Exact Differential Equation - Definition

Definition

Given a simply connected and open subset D of R2 and two functions I and J which are continuous on D then an implicit first-order ordinary differential equation of the form

is called exact differential equation if there exists a continuously differentiable function F, called the potential function, so that

and

The nomenclature of "exact differential equation" refers to the exact derivative of a function. For a function, the exact or total derivative with respect to is given by

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