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Homework Help: Question involving the solution to a Lagrange Differential Equation

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data

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

    Let y' = P
    taking d/dx and rearranging gives

    dx/dP - xf'(P)/{P - f(P)} = g'(P)/(P - f(P))

    a 1st order linear differential equation in standard form.

    2. Relevant equations

    When I attempt to solve by the suggested standard method, I end up with the following integral:

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

    3. The attempt at a solution
    I'm at a loss as how to go about integrating it.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 5, 2010 #2

    gabbagabbahey

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    Try the substitution [itex]u(p)=p-f(p)[/itex]
     
  4. Apr 5, 2010 #3
    I did and I got

    [tex]\int dP/u(P) - ln|u(P)|[/tex]
    What do I do with the 1st term?
     
  5. Apr 12, 2010 #4

    gabbagabbahey

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    I don't think you can simplify it any further without knowing what [itex]f[/itex] is. At least your integral no longer involves [itex]f'[/itex] though.
     
  6. Apr 13, 2010 #5
    P = y' ; y' = dy/dx I believe.

    The following site lays it out: http://www.newcircuits.com/articles.php
    under Lagrange differential equation.

    I was lead to this site after setting up the Euler-Lagrange equations in r,phi,theta, and became curious as to how to solve them or what kind of solutions they have. ie exact, series. Thanks.
     
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