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Math Help - Non-Exact Equation - Integrating Factor

  1. #1
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    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!

    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
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  2. #2
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    Krizalid's Avatar
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  3. #3
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    Beauty thanks Kryzalid!
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