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integrating factors

 
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Sep4-05, 10:46 PM   #1
 

integrating factors


how do you spot that a D.E. needs an integrating factor, besides experience?
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Sep5-05, 05:40 AM   #2
 
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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.
Sep5-05, 05:59 AM   #3
 
thanks! :)
Sep6-05, 07:13 PM   #4
 
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integrating factors


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

The hard part is finding that integrating factor.
Dec27-05, 03:05 PM   #5
 
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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".
Dec28-05, 07:38 AM   #6
 
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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.
Dec28-05, 07:48 AM   #7
 
thank you!!!
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