1. A nonlinear dynamic system is characterized by the following differential equation: j = 2 y + y2 j + ju 8 where u(t) is the input to the system, while y(1) represents the system output. (1) Lincarize the system at the vicinity of y(0) = 4, y(0) = 0 and u(0) = 0. (ii) Check the stability of the linearized system. (iii) Find the homogeneous and non-homogeneous responses for unit step input. 1. A nonlinear dynamic system is characterized by the following differential equation: j = 2 y + y2 j + ju 8 where u(t) is the input to the system, while y(1) represents the system output. (1) Lincarize the system at the vicinity of y(0) = 4, y(0) = 0 and u(0) = 0. (ii) Check the stability of the linearized system. (iii) Find the homogeneous and non-homogeneous responses for unit step input