A differential equation of the form
where P and Q are given functions. One method of solution is to multiply both sides of the equation by an integrating factor μ(x), given by
μ(x)= exp (∫P(x) dx).
This choice is made because then the left-hand side of the equation becomeswhich is the exact derivative of μ(x)y, and the solution can be found by integration.
In the case where Q(x)=0, this can also be treated as a separable-variable first-order differential equation.