# Integrating factors

how do you spot that a D.E. needs an integrating factor, besides experience?

Zurtex
Homework Helper
If you're talking about 1st order O.D.Es, it's if you can get it of the form:

$$\frac{dy}{dx} + Py = Q$$

Where P and Q are functions of x.

thanks! :)

HallsofIvy
Homework Helper
If it's not already exact, it needs an integrating factor!

The hard part is finding that integrating factor.

mathwonk
Homework Helper
2020 Award
it is just an extension of integration by parts, i.e. trying to use the product rule. "there are no new ideas under the sun".

HallsofIvy