Consider the differential equation y" = -(y')^2 - y + ln(x), 1 lessthanorequalto x lessthanorequalto 2 with the boundary conditions y(1) = 0, y(2) = ln 2. Show that the exact solutions is y(x) = ln 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 z_1 = 1, z_2 = 0.5. You may 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