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Homework Help: Final round: Integrating factors

  1. May 13, 2007 #1

    ssb

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    1. The problem statement, all variables and given/known data
    Final round I promise!!!!

    Is there some sort of trick that can be applied to the following equation so that it is easier to process?
    [tex]\frac{dy}{dt}=\frac{1}{t+y},\:y(-1)=0[/tex]

    3. The attempt at a solution

    Somebody told me that the equation can be made easier by reinterpreting it with y as the independent variable and t as the dependent variable. I still have a vacant look about my face now as I did back then.

    I know that [tex]\frac{dy}{dt}=\frac{1}{\frac{dt}{dy}}[/tex] but when I try to apply it to my initial equation, I get the same thing I started with.
     
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  3. May 13, 2007 #2

    Dick

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    'Somebody' is right. It turns the equation into 1/t'=1/(t+y). Or t'=t+y. That does look a bit simpler, right?
     
  4. May 13, 2007 #3

    ssb

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    Then you just solve it the normal way as if t' were y'? I dont mean rename everything but just work the problem through solving for f(y) instead of y(t)???

    Just fyi I love you.
     
  5. May 13, 2007 #4

    Dick

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    Exactly........
     
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