Differential Equations Workbook For Dummies®

12.6. Finding Solutions with the Help of Integrating Factors

Whenever you see a differential equation like the following:

M(x, y) dx + N(x, y) dy = 0

but it isn't exact — that is, this statement is true:

then you can try to find an integrating factor — μ(x, y) — such that the differential equation changes form to

μ(x, y)M(x, y) dx + μ(x, y)N(x, y) dy = 0

and becomes exact.

If you want a Web-based review on finding integrating factors, check out www.sosmath.com/diffeq/diffeq.html, look for the First Order Differential Equations bullet, and click the Integrating Factor technique bullet.