Question

Find the \(L(e^{2t} (1+t)^2)\).

(a) \(\frac{1}{s-2}+\frac{2}{(s-2)^3} + \frac{2}{(s-2)^2}\)

(b) \(\frac{⁡3}{s-2}+\frac{2}{(s-2)^3} + \frac{2}{(s-2)^2}\)

(c) \(\frac{1}{s-2}+\frac{2}{(s+2)^3} + \frac{2}{(s-2)^2}\)

(d) \(\frac{1}{s-2}+\frac{2}{(s-2)^3} \)

This question was addressed to me by my college director while I was bunking the class.

My query is from Table of General Properties of Laplace Transform in chapter Laplace Transform of Engineering Mathematics

Answer 1

Correct answer is (a) \(\frac{1}{s-2}+\frac{2}{(s-2)^3} + \frac{2}{(s-2)^2}\)

Explanation: In the given question,

\(L((1+t)^2 )=L(1+t^2+2t)\)

\(=\frac{1}{s}+\frac{2}{s^3}+\frac{2}{s^2} \)

\(L(e^{2t} (1+t)^2)=\frac{1}{s-2}+\frac{2}{s-2^3} + \frac{2}{(s-2)^2}\).——————–By the first shifting property