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
Read more about this topic: Exact Differential Equation
Famous quotes containing the word definition:
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)