GATE ME 2023 Set 1 — Question 36
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Engineering Mathematics → Differential Equations → Laplace Transforms & Applications
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Question
Which one of the options given is the inverse Laplace transform of ? denotes the unit-step function.
Correct answer
(A) (-1 + (1)/(2) e^(-t) + (1)/(2) e^t) u(t)
Solution
Let .
Using partial fraction decomposition:Solving for coefficients:
Taking the inverse Laplace transform:This matches option (A).
Using partial fraction decomposition:Solving for coefficients:
Taking the inverse Laplace transform:This matches option (A).
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