# Integrating factors

## Main Question or Discussion Point

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

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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
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
Homework Helper
I'm not sure what you mean by "needs" an integrating factor. Every first order differential equation has an integrating factor but it may be very difficult to find. That's what I meant when I said before "If it's not already exact, it needs an integrating factor!"

If a first order differential equation is linear then there is a simple formula for the integrating factor. I presume that was what Zurtex meant.

thank you!!!