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June 29th, 2018, 11:34 AM   #1
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Simple short question on differentials

Does the equation below have an integrating factor? If not, why? If yes, why?
$\displaystyle X''+p(x)X'+q(x)X=f(x)$

Last edited by skipjack; June 29th, 2018 at 10:20 PM.
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June 29th, 2018, 11:56 AM   #2
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Answer is yes because it is a linear equation and every linear equation has a solution by integrating factor method. Sometimes this is called the variation of constants method when applied to higher order equations but they are exactly the same method.
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June 29th, 2018, 01:27 PM   #3
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Integrating factors can be used in general for first order equations. For higher order some work will be required.
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