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(4) Show that L[u(v — 2)](s) = −²³. -38 +386

(4) Show that L[u(v — 2)](s) = −²³. -38 +386

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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Number 4

For problems # 1 - 5 show the Laplace Transform for the given function is what the chapter states (1) Use integration by parts and the definition of the Laplace transform to justify why L{y'} = s£{y} − y(0) for s> 0 whenever y(t) is bounded. 2 (2) Show that L[x²e²](s) = (s-1)³ · (3) Show that L[cos(t)](s) = ²+1 (4) Show that L[u(v − 2)](s) = e−²³. (5) Show that L[u(x − 3)x](s) -38 e +3se-3s 82 Solution Solution Solution Solution Solution
Transcribed Image Text:For problems # 1 - 5 show the Laplace Transform for the given function is what the chapter states (1) Use integration by parts and the definition of the Laplace transform to justify why L{y'} = s£{y} − y(0) for s> 0 whenever y(t) is bounded. 2 (2) Show that L[x²e²](s) = (s-1)³ · (3) Show that L[cos(t)](s) = ²+1 (4) Show that L[u(v − 2)](s) = e−²³. (5) Show that L[u(x − 3)x](s) -38 e +3se-3s 82 Solution Solution Solution Solution Solution
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