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

Jaylen Dudley

Jaylen Dudley

Answered question

2022-09-16

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

Answer & Explanation

illpnthr21vw

illpnthr21vw

Beginner2022-09-17Added 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 .
yrealeq

yrealeq

Beginner2022-09-18Added 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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