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Homework Help: Differential Equation, nonlinear, nonexact

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]\frac{dy}{dx}=\frac{2y - x + 7}{4x - 3y -18}[/itex]

    2. Relevant equations

    3. The attempt at a solution
    I tried using v = y/x and got nothing. Same goes for trying to find an integrating factor to make the equation exact. I am given a hint, Find h and k so that the substitution x = u+h, y=v+k transforms the above to a homogenous differential equation. I'm not sure what the means or how I'm supposed to use that. Thanks for any help.
  2. jcsd
  3. Oct 9, 2012 #2


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    Do you see why the v = y/x method didn't work? Do you see why the ##\frac{M(x,y)}{N(x,y)}## functions aren't homogeneous? Can you use the given substitution to get rid of the 7 and -18?
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