1
GATE ME 2023
MCQ (Single Correct Answer)
+2
-0.66
Which one of the options given is the inverse Laplace transform of $\rm \frac{1}{s^3-s}$? 𝑢(𝑡) denotes the unit-step function.
A
$\rm \left(-1+\frac{1}{2}e^{-t}+\frac{1}{2}e^t\right)u(t)$
B
$\rm \left(\frac{1}{3}e^{-t}-e^t\right)u(t)$
C
$\rm \left(-1+\frac{1}{2}e^{-(t-1)}+\frac{1}{2}e^{(t-1)}\right)u(t-1)$
D
$\rm \left(-1-\frac{1}{2}e^{-(t-1)}-\frac{1}{2}e^{(t-1)}\right)u(t-1)$

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