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Steps to solving L{u(t−2)e3t}?

  1. May 31, 2015 #1
    looking for the steps to solving this L{u( t − 2)e3 t}. The problem itself looks like a second shifting theorem problem but i don't know how it's done.

    answer was given as:

    ((e6)(e-2s))/(s-3)
     
  2. jcsd
  3. May 31, 2015 #2

    yjc

    User Avatar

    You can get the answer by applying two properties of the laplace transform. Suppose ##x(t) \leftrightarrow X(s) ##. Then:
    1. ##x(t-a) \leftrightarrow X(s)e^{-as}##
    2. ##x(t)e^{at} \leftrightarrow X(s-a)##

    In fact, you should be able to derive these properties in two or three lines, starting from the definition of the laplace transform. The first is derived by redefining ##t^{'} = t-a##, the second by redefining ##s^{'} = s-a##.
     
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