Explanation Procedure used: The inverse Laplace transform of the function F ( s ) is f ( t ) . If such a function exit, that satisfies L ( f ( t ) ) = F ( s ) . The inverse Laplace transform of F ( s ) is, f ( t ) = L − 1 ( F ( s ) ) Formula: If f ( t ) = U ( t − a ) , then F ( s ) = L ( f ( t ) ) = e − a s s . Property: If L − 1 ( G ( s ) ) = g ( t ) , then L − 1 ( e − a s G ( s ) ) = U ( t − a ) ⋅ g ( t − a ) Linear property of inverse Laplace transforms: If L − 1 ( F ( s ) ) and L − 1 ( G ( s ) ) are exist, then L − 1 ( a F ( s ) + b G ( s ) ) = a L − 1 { F ( s ) } + b L − 1 { G ( s ) } Calculation: Consider the function, F ( s ) = 3 e 6 − s 6 − s Take the inverse Laplace transform: F ( s ) = L − 1 { 3 e 6 − s 6 − s } = − 3 L − 1 {

5th Edition

ISBN: 9780128149485

Author: Abell, Martha L. L.

Publisher: Elsevier Science

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Chapter 8, Problem 37RE

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The inverse Laplace transform for the function 3e6−s6−s.

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Chapter 8, Problem 36RE

Chapter 8, Problem 38RE

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Chapter 8 Solutions

Introductory Differential Equations

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - Prob. 61E Ch. 8.1 - 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The inverse Laplace transform for the function 3 e 6 − s 6 − s .

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The inverse Laplace transform for the function 3e6−s6−s.

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Chapter 8 Solutions