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:
“Im beginning to think that the proper definition of Man is an animal that writes letters.”
—Lewis Carroll [Charles Lutwidge Dodgson] (18321898)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (17721834)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than thisdevoted 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 (18201910)