Laplace Transform

  • Thread starter Turion
  • Start date
  • #1
143
2

Homework Statement



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

Homework Equations





The Attempt at a Solution



$$L\{ { e }^{ -t }*{ e }^{ t }cost\} \\ =L\{ \int _{ 0 }^{ t }{ { e }^{ -\tau }{ e }^{ t-\tau }cos(t-\tau )d\tau } \} \\ =\frac { L\{ { e }^{ t }cost\} }{ s } \\ =\frac { s-1 }{ s[{ (s-1) }^{ 2 }+1] }$$
 

Answers and Replies

  • #2
115
2
Unfortunately it isn't correct. For convolution we have:

##L\{f*g\}=L\{f\}\cdot L\{g\}##
 

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