1. Find the Laplace transform of the following: a) f(x) = x5 e-* b) f(x) = x3 + 3 cos2x 2. Find the inverse Laplace transforms, as a function of x , of the following functions: 1 a) 2s-3 2s+1 b) (s-1)2+7 2 c) (s2 +1) (s-1)2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Find the Laplace transform of the following:
a) f(x) = x5 e-*
b) f(x) = x3 + 3 cos2x
2. Find the inverse Laplace transforms, as a function of x , of the following functions:
1
a)
2s-3
2s+1
b)
(s-1)2+7
2
c)
(s2+1) (s-1)2
Transcribed Image Text:1. Find the Laplace transform of the following: a) f(x) = x5 e-* b) f(x) = x3 + 3 cos2x 2. Find the inverse Laplace transforms, as a function of x , of the following functions: 1 a) 2s-3 2s+1 b) (s-1)2+7 2 c) (s2+1) (s-1)2
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