A process can be modeled by the differential equation:
du/dt = p*u + i*p
with initial conditions, y(0) = -1, y'(0) = 0, and u(0) = 0.
(i) Determine the zero-input response.
(ii) The input u(t) = 10 for t >= 0 is applied to this process. Show that the time to peak Tp for the output y(t) is:
Tp = ln(1) seconds