APPLICATION OF DIFFERENTIAL EQUATIONS IN THE MODELING ECONOMIC PROCESSES
The article deals with the application of ordinary differential equations for modeling and study of economic processes. In this case applied models are used that deal with idealized objects in the form of various kinds of differential equations and their systems. The main principle of constructing such models is the combination of economic theory with the theory of differential equations. As a rule, economic laws are complex non-linear relations between economic quantities, the explicit form of which is difficult to establish directly. In the presence of a stable law, small changes in magnitudes can be approximately replaced by differentials, and nonlinear quantities by their derivatives. The study provides examples of models of economic processes, which are based on ordinary differential equations. The content of practical material focuses on a detailed analysis of the three problems of the economy: advertising efficiency, supply and demand, depending on the rate of price change, market model with predicted prices. Each problem contains a brief description of the necessary economic theory, a model in the form of a differential equation, the solution of this equation, and an analysis of the results obtained. According to the type of mathematical apparatus used in the examples, equations with separated variables, linear equations of the first and second orders are involved.