5) Find the Laplace transform of the following functions sinh at cosh at eat sin bt eat cos bt theat, n = positive integer a 52-a²³ S s² - a²³ s-a s> |a| b (s-a)² + b²¹ s> |a| n! (s-a)n+1¹ (s-a)² + b²¹ s> a s> a s> a

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(5) Mathematical Physics

Topic: Fourier and Laplace Transform and their Applications 

 

5) Find the Laplace transform of the following functions
sinh at
cosh at
eat sin bt
eat cos bt
theat, n = positive integer
a
s².
5²
-
S
-
9²⁹
a²⁹
s-a
s> |a|
b
3
(sa)² + b²
s> |a|
n!
(s-a)n+1
(sa)² + b2'
s> a
s > a
s> a
Transcribed Image Text:5) Find the Laplace transform of the following functions sinh at cosh at eat sin bt eat cos bt theat, n = positive integer a s². 5² - S - 9²⁹ a²⁹ s-a s> |a| b 3 (sa)² + b² s> |a| n! (s-a)n+1 (sa)² + b2' s> a s > a s> a
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