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Integrating factors round 2

  1. May 13, 2007 #1

    ssb

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    1. The problem statement, all variables and given/known data

    [tex]y' (1+e^t) + e^ty = 0[/tex]

    How do I get it in the form

    [tex]y' +f(t)y = f(p) [/tex]

    That is how do apply algebra to this so it is in the proper form to process it?

    3. The attempt at a solution

    Kind of hard to post my attempt. I can move the y' (1+e^2) to the right side then divide both sides by y' but that doesn't make it y' + something, rather y' x something.

    I also tried moving everything to the right and canceling some stuff out but it doesnt seem to work.
     
    Last edited: May 13, 2007
  2. jcsd
  3. May 13, 2007 #2

    Dick

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    Divide both sides by (1+e^t). Then read off f(t). What's f(p)????
     
  4. May 13, 2007 #3
    Try dividing throughout by [itex](1+e^t)[/itex].
     
  5. May 13, 2007 #4

    ssb

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    [tex]f(p)[/tex] becomes

    [tex](e^ty)/(1+e^t)[/tex]

    giving equation


    [tex]y' + (e^ty)/(1+e^t) = 0[/tex]

    Are you saying it is allowed to do this step even though the right hand side is zero? I always thought this was a no-no.
     
  6. May 13, 2007 #5

    Dick

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    You aren't dividing by the RHS. You're dividing by (1+e^t). I'm still bothered by what 'p' is supposed to be. You've got f(t)=e^t/(1+e^t) alright.
     
  7. May 13, 2007 #6

    ssb

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    Gotcha. Thankyou so much. I got messed up a few weeks ago when I was given an assignment by my teacher with the wrong answer key. This is now going well. Thankyou thankyou! Thankyou
     
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