GATE 2020 ME (ME2) – Question 14

Engineering Mathematics · Differential Equations: Initial and boundary value problems, Laplace transforms · 1 mark · Multiple choice

Find the Laplace s-domain solution of $d^2y/dt^2-y=1$, with $y(0)=y^\prime(0)=0$.

$1/[s(s+1)(s-1)]$
$1/[s(s+1)]$
$1/[s(s-1)]$
$1/(s-1)$

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Correct answer: (A) $1/[s(s+1)(s-1)]$

Explanation

Zero initial data give $(s^2-1)Y(s)=1/s$. Therefore $Y(s)=1/[s(s+1)(s-1)]$, the expression in **A**. A nonzero initial value would introduce additional transform terms, but none occur here.