Question: The following function Y(s) = L[y(t)] is obtained applying the Laplace transform to a differential equation representing a system with non-zero initial conditions and input

The following function Y(s) = L[y(t)] is obtained applying the Laplace transform to a differential equation representing a system with non-zero initial conditions and input x(t), with Laplace transform X(s)

(a) Find the differential equation in y(t) and x(t) representing the system.

(b) Find the initial conditions y€²(0)and y(0).

(c) Use MATLAB to determine the impulse response h(t)of this system and to plot it. Find the poles of the transfer function H(s) and determine if the system is BIBO stable.

X(s) s+1 Y (s) s + 2s + 3' s² + 2s + 3

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