The Pfaff Problem
Consider a differential equation of the form(1)
where theare functions of the independent variableplus possibly others, andis the total differential.
Equation (1) is called a Pfaff expression.
In general the value ofdepends 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 containsorvariables it is equivalent to not more than n algebraic equations.