GATE 2017 ME (ME2) – Question 15

Engineering Mathematics · Differential Equations: First order and higher order linear equations, Euler-Cauchy equation · 1 mark · Multiple choice

The Laplace transform of $te^t$ is ______.

$s/(s+1)^2$
$1/(s-1)^2$
$1/(s+1)^2$
$s/(s-1)$

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Show answer and explanation

Correct answer: (B) $1/(s-1)^2$

Explanation

The basic transform is L{t}=1/s². Exponential multiplication shifts s to s−1, so L{t exp(t)}=1/(s−1)², valid for Re(s)>1. Therefore **B**; a shift to s+1 would correspond to exp(−t).