Question

Find the \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\).

(a) e^-t+6e^t+5e^2t

(b) e^-t-e^t+5e^2t

(c) e^-3t-6e^t+5e^2t

(d) e^-t-6e^t+5e^2t

I have been asked this question in exam.

The query is from General Properties of Inverse Laplace Transform in portion Laplace Transform of Engineering Mathematics

Answer 1

Correct option is (d) e^-t-6e^t+5e^2t

To explain: In the given question,

\(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\)

=\(L^{-1} \left (\frac{1}{(s+1)}\right )-6L^{-1} \left (\frac{-6}{(s-1)}\right )+5L^{-1} \left (\frac{-6}{(s-2)}\right ) \)————-Using properties of Partial Fractions

=e^-t-6e^t+5e^2t.