Integrating Factors: Spotting D.E. Need for Factor

[asdf1]

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

 

[Zurtex]

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.

 

[asdf1]

thanks! :)

 

[HallsofIvy]

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

The hard part is finding that integrating factor.

 

[mathwonk]

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]

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.

 

[asdf1]

thank you!