In the following examples, let x(t) denote the input to an LTI system, let y(t) denote its output, and let h(t) denote the impulse response.
1. Consider the system $y''(t) - 4y'(t) + 5y(t) = x'(t) + x(t)$.
e. Find an expression for the output, y(t), when x(t)=u(t) and all initial conditions are zero.
f. Find an expression for the output, y(t), when x(t)=0, y'(0)=0, x(0)=0.
g. This is an LTI system. We previously learned that, for LTI systems, y(t) = x(t) * h(t). Can your solution for 1(e) be expressed in this way? Why or why not?
h. Is this system BIBO stable? Justify your answer using the properties of H(s), and also justify your answer using the properties of h(t).
