The input-output equation characterizing a system of input x(t) and output y(t) is

and zero otherwise.

(a) Find the ordinary differential equation that also characterizes this system.

(b) Suppose x(t) = u(t) and any value of y(0), we wish to determine the steady state response of the system. Is the value of y(0) of any significance, i.e., do we get the same steady-state response if y(0) = 0 or y(0) = 1? Explain.

(c) Compute the steady-state response when y(0) = 0, and x(t) = u(t). To do so first find the impulse response of the system, h(t) using the given input-output equation, and then find y(t) by computing the convolution graphically to determine the steady-state response.

(d) Suppose the input is zero, is the system depending on the initial condition BIBO stable? Find the zero-input response y(t) when y(0) = 1. Is it bounded?

-2((-т), -21 | e е ?)x(т)dr t20 У() — еу(0) +2 0.