1. Using the eigenvalue method, solve the initial value problem. Leave your solution in real-valued form. (b) (a) x1 = x2, x2 = -5x1 - 4x2, x1(0) = 1, x2(0) = 0. Classify the linear system from part (a) and sketch a phase portrait.

Solve the system -1 -6 dx dt 1 -6 with the initial value 4 x(0) = x(t)

Consider the system of non-linear differential equations  dx/dt = x2 - 2x - y2 + 1,  dy/dt = xy - 3x.  What is the complete list of equilibrium points for this system?

A DT system is described by the difference equation y[n] + 1/2 y[n - 1] - 1/2 y[n - 2] = x[n] - x[n - 2]. Express the difference equation in operator notation E. Find the closed form solution of the impulse response h[n] when h[0] = 1, h[1] = -1/2.