Nowadays, computation with numerical methods is widely used for solving system differential equations. Many numerical methods have been used and applied such as, Euler method, Runge-Kutta method, Taylor method and other methods. In this thesis, we use the Taylor method as the main method to solve system differential equations. We build a library with automatic differentiation methods to integrate some differential equations. The library we make consist of mathematical operation methods (addition, division, square root, exponential, subtraction, multiplication). This program builds with Python programming language. We test 10 system differential equations to show that the Taylor method is better than the Runge-Kutta method. Besides that, the test of parameter that we already set up to test the successful of the library. We also test the run time process of integrate that we have made and compared between Runge-Kutta method and Taylor method. From the testing using 2 methods, we found that the Taylor method more time-consuming than the Runge-Kutta method to get the solution. However, the Taylor method is more accurate than the Runge-Kutta method to get the solution. The output of testing are same with the input of each parameter’s especially in integrate method. There are various different number of iterations have been tested and obtained a good result with Taylor method.