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Using laplace transforms to solve IVPplease check work thanks

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    y' - 3y = 13cos(2t)

    y(0)=1


    2. Relevant equations
    y' = sY(s) - y(0)


    3. The attempt at a solution

    heres all my work.. i am confused as to why its not matching book solution.. i think (geussing) that I probably messing up the decomposition step..thanks for any help with this
    https://docs.google.com/open?id=0BwJqUg33PgREVjdEN250WXVTaldod3NublhVc1pEdw
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    sorry almost forgot to include this..book solution is:

    y(t) = 4e^3t - 3cos(2t) + 2sin(2t)
     
    Last edited: Mar 12, 2012
  2. jcsd
  3. Mar 12, 2012 #2

    vela

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    You made a couple of algebra mistakes, one of them due to an omission of parentheses where they were needed.
     
  4. Mar 12, 2012 #3
    thanks for the help..yup i see it: (As+B)(s-3) makes all the difference, giving me C=3, B=4 and A = -3.....now matches book solution.. but have follow-up question..

    If I start solving equation with what I think is a fully decomposed denominator, when denominator could actually be decomposed further, then the answer I get should be identical to the one solved with fully decomposed denomiator, right? so, even though i probably had to solve with more steps because deenominator wasnt fully decomposed, the answers shouls still be the same, true?
     
  5. Mar 12, 2012 #4

    vela

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    Yes, you should ultimately get an equivalent answer. The two results may not be expressed in exactly the same way, but they will be equal to each other.
     
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