Question

Find the inverse Laplace transform of followings..

a) ?(?)=[−3?^(−2?)−3?^(−4?)+4?^(−6?)+3?^(−7?)] / s

b) ?(?)=(?^(−8?))/)?^(2)−4)

c) ?(?)=(7?^(−7?))/?^(2)+64

d) ?(?)=(?^(−2?)(6?−2))/(?^(2)+36)

e) ?(?)=(12)/(?^(2)−9)?−4^?

Answer #1

a.) Find the Laplace transform of ?(?)=1+?(?−5)⋅(?+9)
b.) Find the Laplace transform of?(?)=?(?−4)⋅?^2
c.) Find the Laplace transform of?(?)=?(?−(3?)/2)⋅sin(?)
d.) Find the Laplace transform of ?(?)=?(?−4)⋅?^(−?)

1. Find the Laplace transform of
a.) f(t)=u(t−4)⋅e^t
F(s)=
2. Find the inverse Laplace transform of
a.) F(s)=2e^(−3s)−e^(−2s)−3e^(−6s)−e^(−9s)/s
f(t) =
b.) F(s)=e^(−6s)/s^2−3s−10
f(t) =
c.) F(s)=4e^(−9s)/s^2+16
f(t) =

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 F(s)=
6s^3-15s^2+20s-48/s(s-3)(s^2+4)

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)

a) Find the Laplace Transform of : (?) ???3? cos 2? (??) ? −2?
???2 ?
b) Find the Inverse Laplace Transform of: (?) ?−4 /
?2−4 (??) 4 / s2−2?−3

Find Inverse Laplace Transform
2s/(s-1)^2 (s+1)

find the inverse laplace transform of f(s)=(s^2+1)/(s^2(s+2))

Find the inverse Laplace transform of
(2s+9)/(s^2+19s) where s>0
y(t)=

find the inverse Laplace transform of the given function.
1. F(s) = (8s2 − 4s + 12)/ s(s2
+ 4)
use the Laplace transform to solve the given initial value
problem.
2. y'' − 2y' + 2y = 0; y(0) = 0, y' (0) = 1

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