2. (It is required to use a program to finish this question. Only programs written in C/ C++/Matlab/Ovtave is acceptable. Hand in the code via CCLE. Print your tabulated results and graphs.) Consider the following system boundary value problem: y" = sin(y) 2y on (0,25) (a) Show that the BVP has a unique solution (b) Write the BVP in a systern of first order ODE by letting ui = y, u2 = y. (c) Let x(t, a) be the unique solution to r" = sin(z) + 2z on (0.2.5) Let F(a) := z(25:a)-15. Write down the secant method for the function F Try to solve BVP by using the secant method with initial values ao-1 and on = -0.7. You only need to calculate 3 (new) secant-steps, i.e. a2, o3,a4. Plot the graphs of {x(t; ai)) for i = 1, 2, 3, 4. (For a given a, use the 2-step Adam-Bashforth method method to numerically ap- proximate the solution u 1(t)-z(ta),u2 = r(ta) with a mesh size 0.1. Please use the initial values wo and w by computing w from wo with a 2-nd Taylor series method. Then with o and w, use Adam-Bashforth.)