1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    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...

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook