Project ForgeEngineering Mathematics
Calculus
GATE 2020
Medium
The solution of d²y/dt² − y = 1, which additionally satisfies y|(t=0) = dy/dt|(t=0) = 0, in the Laplace s-domain is
- 1/[s(s+1)(s−1)]
- B1/[s(s+1)]
- C1/[s(s−1)]
- D1/(s−1)
Explanation
Taking the Laplace transform with y(0)=y′(0)=0: s²Y(s) − Y(s) = 1/s, so Y(s)(s²−1) = 1/s, giving Y(s) = 1/[s(s²−1)] = 1/[s(s−1)(s+1)] — option (A).
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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