Problem 3. The higher order differential equation and initial conditions are shown as follows: dy dy 3: + 2y = t + cos(t), y(0) = 0.5, y'(0) = 1. dt dt? (a) differential system, including initial...

PART B

Extracted text: Problem 3. The higher order differential equation and initial conditions are shown as follows: dy dy 3: + 2y = t + cos(t), y(0) = 0.5, y'(0) = 1. dt dt? (a) differential system, including initial conditions. Transform the above initial value problem into an equivalent first order (b) Express the system in (a) in matrix form, write the initial condition in vector form. (c) Using the second order Runge-Kutta method as follows Ý: + hF(t;, ji) h Ti+1 Y:) + to solve system in (b) with step size h, what is the matrix form of the iteration formula? (You do not need to combine the above two equations into one equation)