1) [25 pt] Dorfman & Daoutidis 6.13 6.13 In the course of solving a boundary value problem for some function c(x) using centered finite differences, there is a subfunction for computing the residuals that has the following structure: + 2 . 5 function out = problem6_13 n = length(c); dx = 2/(n-1); R(1,1) = c(1) - 1; for i = 2:1-1 R(1,1) = c(i+1) - 2*c(1) + c(1-1) - (dx)^2*c(i)^2; end Ron, 1) = 2*c(n-1) + 2* (dx-1)*c(n) -(n) 2*dx^2; out = R; 7 Answer the following questions about this problem. (a) If x1 = 0, what is Xn? (b) What is the ordinary differential equation solved by this program? (c) What are the boundary conditions? (d) Write a subfunction that takes the vector c as its input and returns the Jacobian needed for the Newton- Raphson solution of the