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Laplace transform on specific interval

  1. Mar 20, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to solve the following ODE using the laplace domain:
    y' + 4y + 20(integral from 0->t)y(t)dt = 34e^-t on the interval 0<t<4 (y(0) = 0)


    2. Relevant equations
    I can solve the ODE fine, no problems. But I'm a little confused on how to evaluate it strictly on this interval. Would I need to utilize the step function somehow?


    3. The attempt at a solution
    This is what I did so far:
    (sY(s) - 0) + 4Y(s) + 20Y(s) / s = 34 / (s + 1)
    but this is not taking into account the interval...
     
  2. jcsd
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