Develop an M-file to solve a single ODE with the fourth-order RK method. Design the M-file so that it creates a plot of the results.

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Develop an M-file to solve a single ODE with the fourth-order RK method. Design the M-file so that it creates a plot of the results. Test your program by using it to solve Prob. 22.2. Employ a step size of 0.1.

Data From Problem 22.2

Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1. Display all your results on the same graph.

(a) Analytically.
(b) Using Euler’s method.
(c) Using Heun’s method without iteration.
(d) Using Ralston’s method.
(e) Using the fourth-order RK method.

dy dx =(1+4x)y