Question

Inverse Laplace transform of \(\frac{1}{(s+1)(s-1)(s+2)}\) is?

(a) –^1⁄2 e^t + ^1⁄6 e^-t + ^1⁄3 e^2t

(b) –^1⁄2 e^-t + ^1⁄6 e^t + ^1⁄3 e^-2t

(c) ^1⁄2 e^-t – ^1⁄6 e^t – ^1⁄3 e^-2

(d) –^1⁄2 e^-t + ^1⁄6 e^-t + ^1⁄3 e^-2

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

My question is taken from Laplace Transform by Properties topic in division Laplace Transform of Engineering Mathematics

Answer 1

Right answer is (b) –^1⁄2 e^-t + ^1⁄6 e^t + ^1⁄3 e^-2t

To explain I would say: Given, \(F(s)=\frac{1}{(s+1)(s-1)(s+2)}=\frac{-1}{2(s+1)} +\frac{1}{6(s-1)}+\frac{1}{3(s+2)}\)

Hence, inverse laplace transform is \(f(t)=-\frac{1}{2} e^{-t}+\frac{1}{6} e^t+\frac{1}{3} e^{-2}\)