Consider the initial value problem:
y" + 2y²y" - yy = sint
y(0) = y'(0) = 0, y" (0) = 1.
3.1) Write the higher order ODE as an initial value problem of a system of first-order ODES. 3.2) State (without proof) the formula for the fourth-order Runge-Kutta method in vector form. 3.3) Use the fourth-order Runge-Kutta method to approximate the solution y(1) with stepsize h = 0.5. Perform the calculations correctly to four decimals.