Consider a differential equation of the form
(1)
where the
are functions of the independent variable
plus possibly others, and
is the total differential.
Equation (1) is called a Pfaff expression.
In general the value of
depends on the path of integration. When it does, (1) is called an inexact differential.
Whendoes not depend on the path of integration, (1) is an exact or perfect differential equation (1) is integrable.
Pfaff's problem deals with the case when (1) is not integrable. If it contains
or
variables it is equivalent to not more than n algebraic equations.