Explanation The given function is ( s + 1 ) 2 ( s + 2 ) 4 . By partial fraction, the given function becomes, ( s + 1 ) 2 ( s + 2 ) 4 = A s + 2 + B ( s + 2 ) 2 + C ( s + 2 ) 3 + D ( s + 2 ) 4 Solve the above equation and obtain A = 0 , B = 1 , C = − 2 and D = 1 . 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 { ( s + 1 ) 2 ( s + 2 ) 4 } = L − 1 { 1 ( s + 2 ) 2 − 2 ( s + 2 ) 3 + 1 ( s + 2 ) 4

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 4.3, Problem 20E

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The inverse Laplace transform of a given function.

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Chapter 4.3, Problem 19E

Chapter 4.3, Problem 21E

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Chapter 4 Solutions

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The inverse Laplace transform of a given function.

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