1. Linear Shooting Method for a Two-point Boundary Value Problem

Consider the differential equation y" = y' + 2y + cos (x), for 0 lessthanorequalto x lessthanorequalto pi/2, with boundary conditions y(0) = -0.3, y(pi/2) = -0.1. Show that the exact solution is y(x) = sin(x) + 3 cos(x))/10. Implement the shooting method for this problem in Matlab. Use Matlab solver ode45, with your choice of error tolerance. You can check your answer by comparing it with the exact solution. Plot your solution, and also the error