1. Apr 13, 2009 #1

   macaroni

   

   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?

    

   macaroni, Apr 13, 2009
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3. Apr 13, 2009 #2

   Billy Bob

   

   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.

    

   Billy Bob, Apr 13, 2009

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