Problem 3 (Systems of Differential Equations) For ordinary differential equation x" (t) + 4x' (t) + 5x(t) = 0 with initial conditions x(0) = 3 and x'(0) = -5, a) Use the four order Runge-Kutta method with step size h = 0.1 to solve the differential equation over the interval [0, 5] in MATLAB. HINT: By defining y = x', the second order ODE can be written as a set of first order ODE (which you now know how to handle) given by x' = y (Eq. 1) y' = -5x - 4y Eq. (2) with initial conditions x(0) = 3 and y(0) = -5. These two first order ODES can then be solved simultaneously the four order Runge-Kutta method with step size h = 0.1. The function y(t)=x'(t), is just an intermediate step needed to compute the function x(t) we are solving for.. b) Compare the numerical solution with the true solution x(t) = 3e-2t cos(t) + e-t sin(t) in a MATLAB plot over the same interval. (Hint: define y = x')