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How do I take the laplace of this?

  1. Dec 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Find F(S)

    2. Relevant equations
    L[e^(2-t)U(t-2)]

    3. The attempt at a solution
    a = 2

    and using the laplace table I got:

    e^(-2s)/(s-2)

    answer should be:

    e^(-2s)/(s+1)
     
  2. jcsd
  3. Dec 5, 2014 #2

    Mark44

    Staff: Mentor

    ##e^{2 - t} = e^2 \cdot e^{-t}##
    ##\mathcal{L}[e^{at}] = \frac{1}{s - a}##

    Plus, you need to deal with that u(t - 2).
     
  4. Dec 5, 2014 #3

    Orodruin

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    I would not split ##e^{2-t}##, the 2 is useful for using with the Heaviside function to just make the translation, giving the ##e^{2s}## factor of the result.
     
  5. Dec 5, 2014 #4

    Mark44

    Staff: Mentor

    Good point.
     
  6. Dec 5, 2014 #5

    vela

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    What is ##a## supposed to represent?

    What was your thinking in coming up with this?
     
  7. Dec 6, 2014 #6
    Why not work from the definition:
    \begin{align}
    \int_0^{\infty}e^{2-t}\mathcal{U}(t-2)e^{-st}dt &= e^2\int_2^{\infty}\exp[-t(1 + s)]dt\\
    &= \ldots
    \end{align}
     
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