This paper discusses the problem of integrating modern methods of forecasting and modeling complex technical objects into the learning process. As an example, the problem of solving a system of ordinary differential equations is considered, which has significant practical application. In particular, solving a system of differential equations can be an essential part of patents. The neural network method to solve this problem by using Matlab simulation software and visual modeling tool Simulink is considered. Efficient cloud-based solution to ordinary differential equations is presented.