Q3) the discrete time system is given by y[n]=a x[n]. x[n-1] Explain the properties of the system (linear, causal, time invariant, and stable)

3. a) Determine the total solution for n 20 of a discrete-time system characterized by the following difference equation: y[n]+y[n 1]-6y[n-2] =x[n]. for an input x[n] = (-3)"u[n] and with the initial conditions y(-1) = 1 and y(-2) = -1. b) Classify the time invariancy property of the following system with graphical representation: (i) y(n) = nx(n-1), (ii) y(n) = x(2n-1). For graphical representation, let x(n) = {0, 1, 2, 1, 0).

Q1.1. Plot the following discrete-time signal for −2 ≤ n ≤ 2x[n] = 2-nu[n] + n2u[n+2] -delta[n-2]  2. Plot the following continuous-time signal for −1 ≤ t ≤ 2pi x(t) = 1 - t2 when(t < 0) and e-tcos(t) when (t >= 0)   Plot with justifications and reasons without MATLAB please

A. Why do we say the homogenous differential equations represent the natural response of a system? (2) B. Why are transient responses exponential in nature? (3) C. Does "R" have the same effect in the time constant of an RL as well as RC circuit? (1) What is/are the effect(s)? (2) D. What happens when you suddenly apply voltage to a large bank of capacitors? (2 points) E. An inductor cannot keep its energy when disconnected from a circuit, why (2)? What is/are the effect(s)? (3)