A mechanization method on the mixed operation of the numerical solutions, analytic solution, and showing their figures simultaneously for differential equation

In the paper, a new mechanization method on the mixed operation of the numerical solutions, analytic solution (if exist), and showing their figures simultaneously for differential equation and their MATLAB programs are presented. With the aid of computer software MATLAB, Euler's method is chosen to illustrate the validity and advantages of the method. As a result, we can not only see the analytic solution, numerical solutions, and their errors but also observe how step size affects the error of the numerical solutions by a figure. The mechanization method can be also applied to other numerical method.