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- Math 201, Assignment 4

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1) Evaluate the following Laplace Transforms using the table in the textbook.

a)

L {t

3 − sinh(2t)}

b)

L {(t − 2)2

e

4t

}

c)

L {sin2

(kt)}

d)

L {x(t)}

where

x(t) =

1 0 ≤ t < 2
2 2 ≤ t < 4
0 t ≥ 4
2) Show that all bounded functions are of exponential order. [A function
f(x) is bounded if there exists an M > 0 such that |f(x)| ≤ M for all

x in R.]

3) Evaluate the following inverse Laplace Transforms

a)

L −1

s

2

(s + 1)3

b)

L −1

1

s

2 + 4s + 10

4) Use the Laplace Transform to solve the following initial value problem.

y

00 + 4y = e

−t

, y(0) = 2, y0

(0) = 1

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