Question

find the inverse Laplace transform of the given function.

1. F(s) = (8s^{2} − 4s + 12)/ s(s^{2}
+ 4)

use the Laplace transform to solve the given initial value problem.

2. y'' − 2y' + 2y = 0; y(0) = 0, y' (0) = 1

Answer #1

find the inverse Laplace transform of the given function.
1. F(s) = 3 /(s2 + 4)
2. F(s) = 2/ (s2 + 3s − 4)
3.F(s) = (2s + 2)/ (s2 + 2s + 5)

Find the inverse Laplace transform of the function by using the
convolution theorem.
F(s) =
1
(s + 4)2(s2 + 4)
ℒ−1{F(s)}(t) =
t
0
dτ

Use partial fraction decomposition to find the inverse Laplace
transform of the given function.
(a) Y (s) = 2 /(s 2+3s−4)
(b) Y (s) = 1−2s /(s 2+4s+5)
differential eq

Find the inverse Laplace transform L−1{F(s)} of the given
function.
F(s)=(13s2−18s+216)/(s(s2+36))
Your answer should be a function of t.

Find the inverse Laplace transform of F (s) = 1 / s4 (s2 +1)

Find the inverse Laplace transform of the given function.
(Express your answer in terms of t.)
F(s) =
8s2 − 10s + 75
s(s2 + 25)

Find the inverse Laplace transform of the given function.
(Express your answer in terms of t.)
F(s) =
8s2 − 8s + 48
s(s2 + 16)

find laplace transform of f(t) =t^2(sin3t)
find inverse laplace transform f(s) = 2-2e^-s/s^2

Find the Inverse Laplace Transform of the following
functions
(a)
F(s) =4/s(s2+2s+2)
(b)
F(s) =8/s2(s2+2)

Find the inverse laplace transform of:
(s+1)/(s2(s2+1))

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