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Homework Help: Lagrange Differential Equation

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data

    I'm attempting to solve the following equation:

    y = xf(y') + g(y')

    where y' = P

    y = xf(P) + g(P)

    2. Relevant equations

    I can restate the equation as

    dx/dP - x f'(P)/(P - f(P)) = g'(P)/(P - f(P))

    which is a 1st order differential equation in standard form.

    3. The attempt at a solution
    When I attempt to solve I get

    g(P) = [tex]\int f'(P)dp/(P - f(P))[/tex]

    I = [tex]\int g'(P)dp/(P - f(P)) e^{g(P)}[/tex]

    x = e[tex]^{-g(P)} (I + C)[/tex]

    where C is some constant of integration.
    I'm getting bogged down with g(P). If I do u(P) = P - f(P)
    I get g(p) = [tex]\int dP/u(P)[/tex] - ln|u(P)|

    How do I proceed?
  2. jcsd
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