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Homework Help: First-Order integrating factor of the form f(xy)

  1. Feb 22, 2010 #1
    (Moderator's note: thread moved from "Differential Equations")

    M(x,y) + N(x,y)(dy/dx) = 0

    f'(xy) = G(xy)f(xy) where G(xy) = (Nx - My)/(xM - yN)

    Replace xy with a single variable to obtain a simple 1st order differential equation and find f(xy).

    I got to:

    ln|f| = Integral(G(xy)) by seperating the variables

    But I am unsure how to integrate G(xy) with respect to a single variable.

    Any Suggestions?
    Last edited by a moderator: Feb 26, 2010
  2. jcsd
  3. Feb 25, 2010 #2
    What does f'(xy) denote? Is it [tex]\frac{d}{dx}f(xy)[/tex] or [tex]\frac{d}{d(xy)}f(xy)[/tex]
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