THE ROLE OF DIFFERENTIAL EQUATIONS IN OPTIMAL CONTROL THEORY

Abstract.The article examines the relationship between optimal control theory and differential
equations in economic analysis. The article discusses methods for modeling dynamic
economic systems using differential equations, developing optimal management decisions
for them, and applying mathematical solutions to practical economic problems. The article
also discusses the application of the theory of differential equations in economics, explains
the solution of some economic problems using this theory using examples, and describes
methods for constructing and solving their differential models.
Keywords: differential equation, differential model, economics, practical issues.