canonical form

For the ODE 2 dy + 3xy = e-1.5x dx y(0) = 3, estimate y(4) with a step size of 2 using a. Heun's Runge-Kutta 2nd order method b. Midpoint Runge-Kutta 2nd order method c. Ralston's Runge-Kutta 2nd order methodThe state space representation 5 1 0 -3 0 -20 0 y = [0 1 0]x is in which canonical form? O Observer canonical form O Control canonical form O This representation is not a canonical form1} Determining State Equation The transfer function of a linear system is given by 12(s + 1) am = 3(3 + 3x: + 2)2 Write the state equations in a] The Controllable Canonical form b) The Observable Canonical form :1 Can you write It in Diagonal Canonical form. Why? {1) If your answer to part c is NO, please find closest form to diagonal Canonical form. [Namely Jordan Canonical Form} Select all strategies that you can use to improve the solution of a first order ordinary differential equation, starting from a base case of Euler's method: Use fourth order Runge Kutta method Use Heun's method Use second order Runge Kutta method O Increase the step size Use first order Runge Kutta method O Decrease the step size