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Another ODE

  1. Nov 22, 2009 #1
    Need help with solving this DE.

    1. The problem statement, all variables and given/known data

    [tex](x e^{\frac{y}{x}} + 2x^2 y)dy - y e^{\frac{y}{x}}dx = 0[/tex]

    2. Relevant equations

    3. The attempt at a solution

    Well, I don't even know where to start. It's not exact, and I can't make it exact with an integrating factor. All of this y/x in here makes me think that maybe I need to make a substitution here, but I can't just use it like that because it wouldn't work.
    Any ideas?
  2. jcsd
  3. Nov 22, 2009 #2


    Staff: Mentor

    I would start with v = y/x. I can't guarantee that it would work, since I haven't worked the problem, but it might be what you need to get an exact equation.

    The substitution v = y/x is equivalent to y = vx, so y' = v + v'x.
  4. Nov 28, 2009 #3
    Try using the substitution v = x/y which is equivalent to vy = x

    So dx/dy = v + y*dv/dy

    Give it a try and see if it works.
  5. Nov 28, 2009 #4
    Yes it was, but I also had to make a substitution for y, missed it the first time.
    Got it right now.

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