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GATE 2019 BT – Question 49

Engineering Mathematics · Differential Equations: First order ODEs, higher order ODEs with constant coefficients, Cauchy and Euler equations, Laplace transforms · 2 marks · Multiple choice

Find the Laplace transform of $f(t)=t^2+2t+1$.

  1. $1/s^3+3/s^2+1/s$
  2. $4/s^3+4/s^2+1/s$
  3. $1/s^3+2/s^2+1/s$
  4. $2/s^3+2/s^2+1/s$

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Correct answer: (D) $2/s^3+2/s^2+1/s$

Explanation

Use linearity and $\mathcal L\{t^n\}=n!/s^{n+1}$. The three terms yield 2/s³, 2/s² and 1/s respectively. Their sum is D, for Re s > 0.

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