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Integrating a differential equation

  • Thread starter macaroni
  • Start date
  • #1
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Homework Statement



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

answer: Cy = x^2 + y^2

Homework Equations





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?
 

Answers and Replies

  • #2
392
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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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