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

This choice is made because then the left‐hand side of the equation becomes the 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.