The role of differential equations is shown in this article when training in mathematical modeling. The differential equations serving as significant mathematical models are given. Recommendations about a technique of solution of technical tasks with application of theory of ordinary differential equations are made: analysis of statements of problem and drawing up drawing, drawing up differential equation, integration of workedou t differential equation, definition of common and private decision of equation, role of auxiliary parameters is shown. Considered production situation at Institute of technical profile on material of higher mathematics, which aimed at practical application of them in life. The contents and solution of four applied tasks on differential equations are provided in called article. The conclusion of general law of considered process and numerical determination of required sizes is drawn. The answer on basis of check of a starting position of a task is analyzed. Keywords: differentiated equations, mathematical modeling, continuous education, training, mathematical model, function, system of relations, influence on professional activity, higher mathematics, acceleration, technique. The great value at training to modeling plays how much pupils' imagination about such concept as function, independent ability allocates functional dependences, so that any model includes functions (Gildermag, 1980) and the mathematical model also represents system of relations … (Buslenko, 1964). Ability to apply which should promote mastering by pupils to principal views of forthcoming professional work, has allowed us of training to mathematical modeling at any institute of a technical profile. This training is made on examples of drawing up and research of mathematical models at decision of problems with practical maintenance and consideration of industrial situations. Developed by us includes mathematical models acquaintance with which occurs in a higher mathematics basic course. Realization of put methodical line of training to modeling has demanded didactic processing of these, traditional sections of mathematics, introduction, many mathematical concepts taking into account their orientation on practical application, their representation as mathematical models. Therefore, reduction of differential equations which are significant mathematical models studied in a course of higher mathematics, it is useful to present to their pupils as mathematical models describing course of process and allowing defining it, a condition during moment interesting us. Creation of differential comparison is usually connected with studying of nature of investigated object, demands knowledge of laws of mathematics, physics, chemistry, biology. Means, technique of drawing up of differential equation will be expedient for considering on an example of realization of intersubject communications. Drawing up of differential equation on a statement of problem (physical, chemical or technical) consists in definition of mathematical dependence between variables and their increments (Ponomarev, 1962). In some cases differential equation turns out without consideration of increments - at expense of