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GATE 2015 EE (EE2) – Question 14

Engineering Mathematics · Differential Equations: First order equations, Higher order linear differential equations, Variation of parameters, Cauchy and Euler equations, Partial differential equations, Separation of variables · 1 mark · Multiple choice

Given the Laplace transform of $f(t)=2\sqrt{t/\pi}$ is $s^{-3/2}$, the transform of $g(t)=\sqrt{1/(\pi t)}$ is

  1. $3s^{-5/2}/2$
  2. $s^{-1/2}$
  3. $s^{1/2}$
  4. $s^{3/2}$

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Show answer and explanation

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

Explanation

Differentiate f: $f\prime(t)=1/\sqrt{\pi t}=g(t)$ for positive t. Since f(0)=0, the Laplace differentiation property gives G(s)=sF(s)−f(0).

Hence G(s)=s·s^−3/2=**s^−1/2, B**. The integrable singularity at t=0 is consistent with this transform.

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