1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted