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Homework Help: Separation of variables help

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    use separation of variables to solve the differential equation x^2dy/dx=y-xy

    with the initial condition of y(-1)=-1

    2. Relevant equations



    3. The attempt at a solution

    after i separated and integrated i got the answer y=e^(-1/x-lnx+c)

    the answer in the book is y=e^-(1+1/x)/x

    i can't figure out how they got to that even after i plugged in -1 for x and y

    some help would be greatly appreciated
     
  2. jcsd
  3. Feb 5, 2012 #2

    jamesrc

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    You've done the calculus correctly, now you need to do a little algebra.

    Hint: what's e^(-ln x)?
     
  4. Feb 5, 2012 #3

    SammyS

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    [itex]\displaystyle e^{-1/x-\ln(x)+C}=e^{-1/x}e^{-\ln|x|}e^C[/itex]
    [itex]\displaystyle =e^{-1/x}(1/x)e^C[/itex]​
    Does that help?
     
  5. Feb 5, 2012 #4
    well i think it would be x^-1 so then that would give me the x in the denominator then plugging in the initial values i should get c=1?
     
  6. Feb 5, 2012 #5

    SammyS

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    e0 = 1
     
  7. Feb 5, 2012 #6
    ok thanks for the help i didn't remember that you could rewrite the e functions that way...
     
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