Page 42 - LAPLACE TRANSFORM

Example 2

Find the Laplace Transform using Multiplication by of

the followings:-

e t.
at
L
{ }
at
f(t) = e

1
[ tf )(L ]= =n 1,
s − a


at
e t.
L
{ } −= d  1  Differentiate

ds  − as 
 1 
= (− ) − 2 

 (s − ) a 
1
=
(s − ) a 2

f (x ) = (s − ) a − 1

f ' (x ) = − ( 1 s − ) a − 1− 1 ) 1 ( = − ( 1 s − ) a − 2

= − 1
(s − ) a 2

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