MATLAB CODE:

Solve exercise problem 28.19 from your textbook (Chapra and Canale 7th edition) using classical Runge-Kutta 4 th order method, by writing a MATLAB code. The details of this program is given in the next paragraph. The IVP given in the exercise problem is a second order differential equation, so you must first reduce it to a system of two first order differential equations (auxiliary variable and auxiliary equation) and then solve this system using classical RK-4 method in MATLAB. You must show this step (auxiliary variable and auxiliary equation) in your problem write up. You must also solve for only the first step by hand calculations and check to see if it is same as the solution generated by your MATLAB program. Use a step-size ?z = h = 1 meter. MATLAB program details: Your program will solve a system of two first order ODEs with given ICs (which is all shown in your write up) using classical RK-4 method from z = 0 to z = L ==height of the sailboat mast, using a step-size h = 1 meter. Thus, your program will generate values of the deflection y for every meter from z = 0 to z = L. You must save all this data and plot it. Even though deflection y is a function of the sailboat mast z, plot z as a function of y (so, sailboat mast z must be on the y-axis and deflection y must be on the x-axis of your plot). Optional: You may check your solution by using the MATLAB inbuilt function ode45. But note that ode45 will not generate a uniform step-size (mesh), but the solution generated must match very closely with the solution generated from your code.