a) (s+2)/(s^2 + 5s + 13)
b) (s+2)/(s^2 – 5s + 13)
c) (s-2)/(s^2 + 5s + 13)
d) (s-2)/(s^2 – 5s + 13)
Answer: d) (s-2)/(s^2 – 5s + 13)
Explanation: We can use the Laplace transform properties and tables to find the solution. Using the time shift property and the Laplace transform of sin(t), we get L{e^(-2t)sin(3t)} = (s+2)/[(s+2)^2 + 9]. Using partial fraction decomposition, we can simplify this to (s-2)/(s^2 – 5s + 13).