2. Non-linear Shooting Method for a Two-point Boundary Value Prob- em Consider the differential equation with the boundary conditions y(1)0,y(2) In 2 Show that the exact solutions is y(z) = In x Implement the shooting method for this problem in Matlab. Use Matlab solver ode45. Note that this is a non-linear problem, so you need to use a secant iteration. Since the secant iteration converges quickly if the initial guess is good, it is crucial to get a good initial guess. Try the values 21 1, 220.5. You mav choose the tolerance to be 10-9, and maximum number of iterations for the secant method to be 5. Plot the approximate solutions together with the exact solution. Plot also the error 2. Non-linear Shooting Method for a Two-point Boundary Value Prob- em Consider the differential equation with the boundary conditions y(1)0,y(2) In 2 Show that the exact solutions is y(z) = In x Implement the shooting method for this problem in Matlab. Use Matlab solver ode45. Note that this is a non-linear problem, so you need to use a secant iteration. Since the secant iteration converges quickly if the initial guess is good, it is crucial to get a good initial guess. Try the values 21 1, 220.5. You mav choose the tolerance to be 10-9, and maximum number of iterations for the secant method to be 5. Plot the approximate solutions together with the exact solution. Plot also the error