# Non-Exact Equation - Integrating Factor

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• October 10th 2010, 02:08 PM
Kasper
Non-Exact Equation - Integrating Factor
Hey I've got a question here where I need to find an integrating factor to make an equation exact, but it's in two variables and I'm having trouble finding both values!

Quote:

For what values of m and n will $u=x^ny^m$ be an integrating factor for the differential equation

$(-12y+14x)dx + (4x-6x^2y^{-1})dy=0$
To do this i'm using the exactness formula $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$ Which gives me:

$-12(m+1)x^ny^m+14mx^{n+1}y^{m-1}=4(n+1)x^ny^m - 6(n+2)x^{n+1}y^{m-1}$

$-12(m+1)+14m=4(n+1)-6(n+2)$

$m=2-n$

But i'm not sure where to go from here to get another equation to find m and n. A push in the right direction would be awesome. Thanks for your help!

-Kasper
• October 10th 2010, 03:35 PM
Krizalid
• October 10th 2010, 06:03 PM
Kasper
Beauty thanks Kryzalid!