Explanation The given function is 2 s − 1 s 2 ( s + 1 ) 3 . By partial fraction, the given function becomes, 2 s − 1 s 2 ( s + 1 ) 3 = A s + B s 2 + C s + 1 + D ( s + 1 ) 2 + E ( s + 1 ) 3 Solve the above equation and obtain A = 5 , B = − 1 , C = − 5 , D = − 4 and E = − 3 . Use the result L − 1 { 1 s n + 1 } = t n n ! and L − 1 { 1 s − a } = e a t to find the inverse Laplace transform. L − 1 { 2 s − 1 s 2 ( s + 1 ) 3 } = L − 1 { 5 s − 1 s 2 − 5 s + 1 − 4 ( s + 1 ) 2 − 3 ( s + 1 ) 3 } = 5 L

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.3, Problem 19E

To determine

The inverse Laplace transform of a given function.

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Chapter 4.3, Problem 18E

Chapter 4.3, Problem 20E

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The inverse Laplace transform of a given function.

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