Consider the differential equation for lateral positioning of an airplane landing on a carrier: +9 + 31 - 41y = u In equation, y is the lateral position of the airplane and u is a correction input achieved by airplane rudder movement. Use MATLAB for the following: a) Find the transfer function relating Y(s) to U(s). b) What is the characteristic equation associated with this lateral positioning system? c) Find the eigenvalues and the damping ratio. d) Use ode45 to plot if the input is random, use Stoch Input to generate the input function.