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Why are these DEs homogeneous?

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data
    The following DEs are homogeneous and can be solved using a substitution y=ux or v=xy. I can solve them, I'm just don't see how they are homogeneous.

    How is it that with there being an exponent (y/x) that this is homogeneous. I don't see how I could pull out t[tex]\alpha[/tex]

    (x + ye^(y/x))dx - (xe^(y/x))dy = 0

    Same problem with this one

    ydx + x(lnx - lny -1)dy=0

    For both, I can see the powers are the same, but I don't think I completely understand what it means to have a homogeneous differential equation.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 5, 2008 #2
    also this one is bothering me x(dy/dx) = y ln(xy)
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