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Integration help

  1. Dec 4, 2006 #1
    howdy, i uhh solved this problem early in the semester, and now im looking at it like wtf did i do to get the right answer....it says use the 'off the shelf formula' for first order diff eqns.

    its pretty much just integrating now

    y(x) = e^(x) (int[e^(-x)*-sin(2x)dx] + c)

    ans => y(x)= 1/5(sin2x-2cos2x)+c

    thanks in advance
     
  2. jcsd
  3. Dec 4, 2006 #2

    berkeman

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    Staff: Mentor

    Are you sure you transcribed those correctly? What do you get when you differentiate the answer you've listed? Just sin and cos terms, right?
     
  4. Dec 4, 2006 #3
    If [tex] y(x) = e^{x}\int e^{-x}\times -\sin 2x \; dx [/tex]
     
  5. Dec 4, 2006 #4
    ya thats what i dont understand..
     
  6. Dec 4, 2006 #5
    use integration by parts.
     
  7. Dec 5, 2006 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Ignore the ex outside the integral until you have done the integral itself, using integration by parts (twice) as courtigrad said. (Presumably the integration will have a factor of e-x, canceling the ex outside the integral.)
     
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