Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4).
Answer: f(t)=2 cosh 2t-(3/2) sinh 2t
Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4).
Answer: f(t)=2 cosh 2t-(3/2) sinh 2t
I found an alternative answer.
We can first factor (2s - 3)/(s^{2} - 4) into A/(s+2) + B(s - 2). By the solution methods in your book, you should get A = 7/4 and B = 1/4. We know that F(s) = A/(s - a) means that f(t) = e^{-at}, so what you should get for the answer is f(t) = 7/4 * e^{-2t} + 1/4 * e^{2t}.