Solve the following differential equation under the provided conditions. Plot pole locations (roots of denominator of LT), what do they tell you about stability? Plot the response in MATLAB, use appropriate labels. 1. y + 6y + 11y + 12y 0; y(0) = 2, y(0) = 3, all other derivatives 0 at t = 0 2. For the following differential equation find the impulse response i.e. f(t) = unit impulse. Plot the responses in MATLAB, use appropriate labels. Assume all initial conditions to be zero. Determine if the system is stable? Why? Or Why not? Plot pole locations (roots of denominator of LT, Y(s)). y + 6 + 11 + 12y f(t); 3. For the following differential equation find the step response i.e. f(t) = unit step. Plot the responses in MATLAB, use appropriate labels. Assume all initial conditions to be zero. Plot pole locations (roots of denominator of LT). + 6 + 11 + 12y = f(t); 4. Comment: Do all the above problems have same stability? Why or Why not?