Integrating factors

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Main Question or Discussion Point

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

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  • #2
Zurtex
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If you're talking about 1st order O.D.Es, it's if you can get it of the form:

[tex]\frac{dy}{dx} + Py = Q[/tex]

Where P and Q are functions of x.
 
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thanks! :)
 
  • #4
HallsofIvy
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If it's not already exact, it needs an integrating factor!

The hard part is finding that integrating factor.
 
  • #5
mathwonk
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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".
 
  • #6
HallsofIvy
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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.
 
  • #7
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thank you!!!
 

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