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5. (Ci | Show that L{e"t"} = n! in two ways: (s- a)n+1 (a) Use the translation property for F(s). (b) Use formula (6) for the derivatives of the Laplace transform.

5. (Ci | Show that L{e"t"} = n! in two ways: (s- a)n+1 (a) Use the translation property for F(s). (b) Use formula (6) for the derivatives of the Laplace transform.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Brief Table of Laplace Transform f(t) F(s) := L{f}(s) 1 s >0 s > a eat t", n = 0,1,... S-a' n! s> 0 s > 0 sin bt 5² +b² ? Cos bt s> 0 eat tn. n = 0,1, ... n! -a)n+I s-a eat sin bt s> a (s-a)²+b² > (s-a)²+b² > eat cos bt s-a s> a
Transcribed Image Text:Brief Table of Laplace Transform f(t) F(s) := L{f}(s) 1 s >0 s > a eat t", n = 0,1,... S-a' n! s> 0 s > 0 sin bt 5² +b² ? Cos bt s> 0 eat tn. n = 0,1, ... n! -a)n+I s-a eat sin bt s> a (s-a)²+b² > (s-a)²+b² > eat cos bt s-a s> a
5. Gi n! | Show that L{e"t"} = - in two ways: (s - a)»+1 (a) Use the translation property for F(s). (b) Use formula (6) for the derivatives of the Laplace transform.
Transcribed Image Text:5. Gi n! | Show that L{e"t"} = - in two ways: (s - a)»+1 (a) Use the translation property for F(s). (b) Use formula (6) for the derivatives of the Laplace transform.
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