Please show step by step solution. Please answer all the parts.

The higher order differential equation and initial conditions are shown as follows: z 21!- + :42, MO) = 1. 53(0) = 11 9'10): 2 (a) [5pts.] Transform the above initial value problem into an equivalent rst order differential system1 including initial conditions, (b) [2pts.] Express the system and the initial condition in (a) in vector form. (C) [4pts.] Using the second order Runge Kutta method as follows {5* 2 131+ hints) h - e _. 5.2+] = 171' + EiFite 171') + Faint119*\"- to solve system in (b) with step size h, what is the vector form of the iteration formula? (You do not need to combine the above two equations into one equation)