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First order ODE

  1. Jun 28, 2013 #1

    FeDeX_LaTeX

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    I have the differential equation:

    [tex] 4(2x^2 + xy) \frac{dy}{dx} = 3y^2 + 4xy[/tex]

    The only thing I could see working is a substitution, but I can't work out which one to use. I've tried letting v = xy, or v = y/x, but neither of those seem to produce anything useful. Can anyone give me a hint?
     
  2. jcsd
  3. Jun 28, 2013 #2
    i thought it was supposed to be y=xv... thats for the homogeneous ones i think. i am not expert though i am in the class right now myself.
     
  4. Jun 28, 2013 #3

    FeDeX_LaTeX

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    You're right, y = vx does work... sorry, idiotic me didn't even check it properly. Thanks!
     
  5. Jun 28, 2013 #4

    D H

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    Refactor the left hand side to 4x(2x+y)dy/dx. This suggests trying u=2x+y. This will simplify nicely, and should in turn suggest trying v=u2.
     
  6. Jun 28, 2013 #5

    FeDeX_LaTeX

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    Thanks, that worked out even better -- I think that may have been the intended solution.
     
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