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GATE 2018 CE (CE2) – Question 37

Engineering Mathematics · ODE: First order and higher order linear equations, Euler-Cauchy equations, initial and boundary value problems · 2 marks · Multiple choice

For $f(t)=e^{at}$, $t\ge0$, constant a and $s-a>0$, its Laplace transform F(s) is ______.

  1. $1/(s+a)$
  2. $1/(s-a)$
  3. $1/(a-s)$
  4. $\infty$

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Correct answer: (B) $1/(s-a)$

Explanation

By definition, $$F(s)=\int_0^\infty e^{at}e^{-st}\,dt=\int_0^\infty e^{-(s-a)t}\,dt=\frac1{s-a}.$$ Convergence requires the stated condition s − a > 0. Answer B.