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Math Help - Verify that ... is an integrating factor?

  1. #1
    Super Member fardeen_gen's Avatar
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    Verify that ... is an integrating factor?

    By differentiating the equation:
    \int \frac{f(xy) + F(xy)}{f(xy) - F(xy)}\cdot \frac{d(xy)}{xy} + \ln \left(\frac{x}{y}\right) = c
    verify that:
    \frac{1}{xy\{f(xy) - F(xy)\}}
    is an integrating factor of f(xy)\ y\ dx + F(xy)\ x\ dy = 0
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  2. #2
    Super Member Rebesques's Avatar
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    Call the intergrating factor P. Differentiate the given equation to verify
    <br /> <br />
\frac{\partial }{\partial y}(P(x,y)f(xy)y)=\frac{\partial }{\partial x}(P(x,y)F(xy)x).<br /> <br /> <br />
    Last edited by Rebesques; May 5th 2009 at 09:40 AM. Reason: right hand side should be d/dx
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