Can the Inverse Finding the Laplace transform of (2s+1)/(s(s+1)(s+2)) without using partial fractions?

Jaylen Dudley 2022-09-16 Answered
Can the Inverse Finding the Laplace transform of 2 s + 1 s ( s + 1 ) ( s + 2 ) without using partial fractions?
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Answers (2)

illpnthr21vw
Answered 2022-09-17 Author has 17 answers
It is not right away the convolution of two functions but you can split into two fractions and use convolution on each one and add the results .

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yrealeq
Answered 2022-09-18 Author has 1 answers
F ( s ) = 2 s + 1 s ( s + 1 ) ( s + 2 )
With s s 1 2
2 s ( s 2 1 4 ) ( s + 3 2 ) = s ( s 2 1 4 ) 2 s + 3 2 = 0 x cosh 1 2 t 2 e 3 2 t   d t = 0 x e t + e 2 t   d t = e x 1 2 e 2 x + 3 2
then from F ( s c ) = e c x f ( x ) we have
f ( x ) = e 1 2 x ( e x 1 2 e 2 x + 3 2 ) = e 3 2 x 1 2 e 5 2 x + 3 2 e 1 2 x

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