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Again Sep of Vars

  1. Feb 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Find implicit and explicit solution for

    [tex]x^2\frac{dy}{dx}=y-xy[/tex] when y(-1)=-1

    So far I have:


    [tex]\Rightarrow x^{-2}(1-x)dx=\ln y+C[/tex]

    [tex]\Rightarrow (x^{-2)-x^{-1})dx=\ln y+C[/tex]

    [tex]\Rightarrow -\frac{1}{x}-\ln x=\ln y+C[/tex]

    With the initial values, (-1,-1) are outside of the domain. What gives? My integration looks good to me. What am I missing?

  2. jcsd
  3. Feb 1, 2008 #2

    Ben Niehoff

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    Science Advisor
    Gold Member


    [tex]\int \frac{du}{u} = \ln |u| + C[/tex]

    Assuming everything else is correct, that might be your mistake.
  4. Feb 1, 2008 #3
    Oh, yes, that looks like it would clear up the problem. Thanks Ben. The integration looked a little to easy to be getting the best of me. It's always the details...

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