APPLICATION OF THE RICCATI METHOD IN SOLVING DIFFERENTIAL EQUATIONS

Otajonova Sitorabonu Shukhratovna

Authors

Otajonova Sitorabonu Shukhratovna Asia International university General technician sciences department intern teacher

Keywords:

Keywords: Riccati differential equation, nonlinear differential equation, substitution method, linearization, ordinary differential equations, analytical solution, mathematical modeling.

Abstract

Differential equations occupy a central place in modern mathematics and applied sciences because they provide mathematical models for numerous physical, engineering, and biological processes. Among nonlinear first-order differential equations, the Riccati differential equation represents one of the most important classes due to its wide applicability and unique transformation properties. Although the Riccati equation is nonlinear, it can be reduced to a linear differential equation when a particular solution is known. This transformation significantly simplifies the solution process and allows the application of classical analytical methods.

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