Consider the Runge-Kutta method for solving te ODE dy/dx = f(x, y) x_n + 1 = x_n

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Consider the Runge-Kutta method for solving te ODE dy/dx = f(x, y) x_n + 1 = x_n + h k_1 = f(x_n, y_n) k_2 = f(x_n + h/2, y_n + hk_1/2) k_3 = f(x_n + h/2, y_n + hk_2/2) k_4 = f(x_n + 1, y_n + hk_3) y_n + 1 = y_n + h/6 (k_1 + 2k_2 + 2k_3 + k_4). Write a MATLAB program to implement this algorithm. Test your code by solving the initial value problem dy/dx = 1/3 y(8 - y) y(0) = 1 on the interval 0 lessthanorequalto x lessthanorequalto 5 with N = 50 grid points. Find the exact solution of the given IVP and plot it together with the approximate solution calculated using your code. Email the MATLAB code and figure to the TA.

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