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Separable Equation

  1. Sep 14, 2008 #1
    1. The problem statement, all variables and given/known data
    Solve y'=y^2/x , y(1)=1 and give the largest x-interval on which the solution y(x) is defined.


    2. Relevant equations



    3. The attempt at a solution
    [tex]dy/dx = y^{2}/x[/tex]
    [tex]\int dy/y^{2}= \int dx/x[/tex]
    [tex]y=1/(1-ln|x|)
    [/tex]

    Therefore, i find intervals [tex](\infty, e), (0,e), (- \infty , -e)[/tex] where y(x) is defined.

    so would the intervals to choose be [tex](\infty, e) & (- \infty , -e)[/tex]??

    Thanks
     
    Last edited: Sep 14, 2008
  2. jcsd
  3. Sep 14, 2008 #2

    tiny-tim

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    Hi 2RIP! :smile:

    erm … what happend to the y2? :rolleyes:
     
  4. Sep 14, 2008 #3
    Oh sorry, i was still learning how to use the latex coding and left it out. But the rest of my solution should be correct.

    Thanks for pointing that out.
     
  5. Sep 14, 2008 #4

    tiny-tim

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    Hi 2RIP! :smile:

    y is defined at x = 0 , isn't it?

    I'm a little confused by the question … the two largest intervals are both infinite …

    I suspect they mean the largest interval containing x = 1.

    I'm not sure, though … :redface:
     
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