Consider the following second-order ODE: from t = 0 to t = 1 with initial conditions...

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Consider the following second-order ODE: from t = 0 to t = 1 with initial conditions d²y dt2 dy +2- dt. y(0) = -1 and y = e +2y=0 dy dt t() 0.2. (8) Answer the following questions: 1. Write the ODE as a system of two first-order ODES. Show steps for full credit. [0.25 pts] 2. Solve the system of two first-order ODEs with the classical fourth-order Runge-Kutta method with h = 0.5. [1 pt] 3. The analytical solution of the ODE is 4 (-cos (1)-sin(t)) 5 (9) (10) Calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. [0.25 pts] Consider the following second-order ODE: from t = 0 to t = 1 with initial conditions d²y dt2 dy +2- dt. y(0) = -1 and y = e +2y=0 dy dt t() 0.2. (8) Answer the following questions: 1. Write the ODE as a system of two first-order ODES. Show steps for full credit. [0.25 pts] 2. Solve the system of two first-order ODEs with the classical fourth-order Runge-Kutta method with h = 0.5. [1 pt] 3. The analytical solution of the ODE is 4 (-cos (1)-sin(t)) 5 (9) (10) Calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. [0.25 pts]