G which is a differential equation describing a linear time-invariant system. a) Write the characteristic equation for this system. b) Find a solution to the characteristic equation above assuming R1=R2=R3=10kΩ, and C1=C2=1 μF. Complete a MATLAB script (HW4_6.m) – replace all "???" with either numerical or text values and plot characteristic modes for t>0. Comment on the possible behavior of the zero-input response of the system. How quickly the zero-input response "dies" out – assume that characteristic mode contributes equally to y0(t) and use 50% amplitude reduction in your analysis. c) Repeat your analysis (part b) for C1=1.0nF. d) Say something interesting, for example, compare the behaviors of the system with different parameters [part (b) and part (c)] – what is the main difference].