Consider the following ODE:

(1) Find a state space representation of this system using the nested integral method.

(2) Find the digital implementation of this system for a sample time using the Backward Euler approximation, using the sample time

(3) Plot the response of the continuous system (until the response dies off or settles) using either Simulink or ODE45, when the system is released from an initial condition

and , with a constant input = 1. Assume = 0.3, = 0.25 =

0.6. Include code and block diagram

y(t)+a1y(t) + a2y(t) = u(t) bou(t) y(t)+a1y(t) + a2y(t) = u(t) bou(t)