How to compute the inverse laplace transform of this term? (-3/(10)s−1/5)/((s+1)^2+1)

Francis Oliver

Francis Oliver

Answered question

2022-10-22

How to compute the inverse laplace transform of this term? 3 10 s 1 5 ( s + 1 ) 2 + 1

Answer & Explanation

indivisast7

indivisast7

Beginner2022-10-23Added 13 answers

L ( y ) = 3 10 s 1 5 ( s + 1 ) 2 + 1
you want to get this into the form. a ( s + 1 ) + b ( s + 1 ) 2 + 1
At which point:
y = a e t cos t + b e t sin t
3 10 ( s + 1 ) + 1 10 ( s + 1 ) 2 + 1
caritatsjq

caritatsjq

Beginner2022-10-24Added 3 answers

Hint. One may write
3 10 s 1 5 ( s + 1 ) 2 + 1 = 3 10 ( s + 1 ) ( s + 1 ) 2 + 1 + 1 10 1 ( s + 1 ) 2 + 1
then one may apply the properties of the inverse Laplace transform to each term

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