What is the laplace transform of the following function f(t)=t^(10) cosh (t)

katdoringlo 2022-09-12 Answered
What is the laplace transform of the following function
f ( t ) = t 10 cosh ( t )
Is there another method that doesn't include differentiating the Laplace transform of cosh t ten times?
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Answers (2)

Hajdiniax
Answered 2022-09-13 Author has 8 answers
f ( t ) = t 10 cosh t = t 10 ( e t + e t 2 ) = 1 2 t 10 e t + 1 2 t 10 e t L ( f ( t ) ) = 1 2 10 ! ( s 1 ) 11 + 1 2 10 ! ( s + 1 ) 11

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tophergopher3wo
Answered 2022-09-14 Author has 5 answers
Yes. Remember that cosh ( t ) = e t + e t 2 . Use this to rewrite f(t) and use a relatively simple Laplace transform for functions of the form t n e a t

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