Exercise 1 Consider the ordinary differential equation d²x dx + dt² dt - 2x = 0. (a) Convert the equation into a system of first order differential equation. (b) Write the system in the form dz(t) = AZ(t), dt where Z: R → R² is vector-valued. (c) Compute the associated fundamental matrix solution for the differential equation in (b). (d) Hence find the general solution of (N). (e) Obtain a solution that satisfies Z(0) = = (7)