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Laplace Transform

  1. Oct 2, 2013 #1
    1. The problem statement, all variables and given/known data

    $$L\{ { e }^{ -t }*{ e }^{ t }cost\}$$

    2. Relevant equations



    3. The attempt at a solution

    $$L\{ { e }^{ -t }*{ e }^{ t }cost\} \\ =L\{ \int _{ 0 }^{ t }{ { e }^{ -\tau }{ e }^{ t-\tau }cos(t-\tau )d\tau } \} \\ =\frac { L\{ { e }^{ t }cost\} }{ s } \\ =\frac { s-1 }{ s[{ (s-1) }^{ 2 }+1] }$$
     
  2. jcsd
  3. Oct 2, 2013 #2
    Unfortunately it isn't correct. For convolution we have:

    ##L\{f*g\}=L\{f\}\cdot L\{g\}##
     
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