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Substitution Differential Equation

  1. Oct 7, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve the given initial value problem.

    2. Relevant equations

    [tex]ydx + x(lnx - lny - 1)dy = 0[/tex]

    3. The attempt at a solution

    I am confused as to what to do as I can't just substitute y=ux or x=vy because they are not homogeneous of the same degree. And I can't use exact because:

    [tex]\frac{\partial M}{\partial y} \neq \frac{\partial N}{\partial x}[/tex]
  2. jcsd
  3. Oct 7, 2009 #2


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    I don't think u=x/y is such a bad start. ln(x)-ln(y)=ln(x/y)=ln(u). I haven't tried to follow it out. But I would definitely start with that.
  4. Oct 7, 2009 #3


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    Are you sure it isn't homogeneous? Remember ln(x) - ln(y) = ln(x/y)
  5. Oct 8, 2009 #4
    I got it thanks for the help.
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