Solve the following differential equations using Laplace Transform technique. D^2y/dt^2 + 4 dy/dt + 3y = 2r(t) where the initial conditions are y = 1 ,dy/dt (0) = 0, and r(t) = 1, t > 1. For the dynamical systems below: d^3c/dt^3 + e d^2c/dt^2 + 3 dc/dt + lc = 6 d^2r/dt^2 + 4 d^3x/dt^3 + 3 d^2x/dt^2 + 4 dx/dt + 12x = d^2 u/dt^2 + 3 du/dt + 2u Determine the transfer function Compute the poles and the zeros Plot the poles and the zeros on the s-plane Are the following MIMO systems controllable? Why or why not? observable? Why or why not? Please set up the matrices and use calculator or software to do computation if needed [x_1 x_2] = [2 0 -1 1] [x_1 x_2] + [1 -1] u and y = [1 1][x_1 x_2]