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Is there an easier way of computing an integrating factor for differential equations? I need help understanding how to calculate those. I know the reason for them but just not familiar with how to compute exponential power functions. Help please

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Do you have some set of particular differential equations in mind? There are lots of types of integrating factors, some more obscure than others. –  mixedmath Jul 3 '11 at 6:25
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For a general first-order DE of the form $f(x,y) dx + g(x,y) dy = 0$, computing an integrating factor is exactly as hard as solving the DE. Only if there happens to be an integrating factor of a special form can you hope to do it directly. –  GEdgar Jul 3 '11 at 12:31
    
Back from recent holiday. Well, I wanted to know if there was some easier way of generating the integration factor without needing to use exponential. :) –  user10695 Jul 6 '11 at 17:45
    
@user10695 The solution is what it is, we cannot change that "by methods". –  AD. Jun 29 '12 at 21:10
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1 Answer

You need to specify which type of differential equation you are trying to solve, i.e. linear, nonlinear, first order, etc.

Since you said exponential, I'm assuming you mean first order linear? (It's the only type I know that has an exponential integrating factor). Simply take the exponential of the coefficient of the linear term. For $y'+P(x)y=Q(x)$, the integrating factor is $e^{ \int P(x)\; dx}$

If that's not the type of diff. eq. you wanted, please specify.

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