Consider the following two-point boundary value problem (BVP) y"(x)-x²y'(x)=(1+x)y(x) = 0, y(0) = 1, y(1)=2. (1) Show that the problem (1) admits a unique solution. (2) Describe the shooting method for solving the two-point BVP (1) (1) Divide the interval [0,1] uniformly into (n+1) sub-intervals each of length h and let x = ih,i=0,1,...,n+1. Denote by yn the approximation of y(xn). (3) Using the shooting method with n = 1 and invoking explicit Euler method for the associated initial value problems with y'(0) = 0 and y'(0) = 1, respectively, compute the approximate value of y(1/2). (4) Describe the finite difference method for solving the BVP (1). (5) Write explicitly the tridiagonal linear system Ay = b, where y = (y1,y2, - - - ‚ Yn), obtained from the finite difference method. (6) Give a sufficient condition on the step size h for which the above linear system admits a unique solution. (7) Show that the global error En = maxi=0,1,...ny(xn) - yn of the finite difference method is in O(h²). (8) Compute the approximate value of y(1/2) obtained from the finite difference method with n = 2.