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Integrating a differential equation

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data

    y' = 2xy/(x^2-y^2)

    answer: Cy = x^2 + y^2
    2. Relevant equations



    3. The attempt at a solution

    dy/dx = 2xy/(x^2-y^2)
    dy = [2xy/(x^2-y^2)]dx

    how do i separate the variables?
     
  2. jcsd
  3. Apr 13, 2009 #2
    In the form 2xy dx + (y^2-x^2) dy, the coefficients are both homogeneous and of degree two, so the substitution y=vx will work. Kind of long way to do it, but it works.
     
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