Tambov: TSTU, 2011. — 80 s . In the study of natural phenomena, the solution of many problems of physics and technology, chemistry and biology, other sciences, it is not always possible to directly establish a direct relationship between the quantities describing a particular evolutionary process. However, in most cases, it is possible to establish a relationship between the values (functions) and the rates of their change relative to other (independent) variables, t. e. find equations in which unknown functions are contained under the derivative sign. Such equations are called differential equations; they serve as an important means of modeling various processes. The purpose of this book is to help students in the formation of their mathematical thinking, in the development of practical solving skills and the study of differential equations describing evolutionary processes in various fields of natural science. In the manual, an attempt is made to develop a modern technological learning tool for solving ordinary differential equations, as well as controlling the learning process. Most of the control tasks have a test form, which allows you to expand the field of control and reduce the time of its implementation. At the same time, the authors do not abandon the traditional form of tasks, which in testology is called tasks with an expanded answer. The structure of the material is as follows: each chapter sets out the basic theoretical information and algorithms for solving typical problems, followed by tasks for active learning. The control unit offers theoretical exercises, tasks for independent decision, and, finally, tasks in the form of tests. The main provisions of the theory and methods of solving problems on the topics "Ordinary Differential Equations", "Systems of Differential Equations". Samples of problem solving and test options for each section are offered, including the final standard tasks.