Analytic General Solutions of the Riccati equation

Abstract

A novel integrability condition for the Riccati equation, the simplest form of nonlinear ordinary differential equations, is obtained by using elementary quadrature method. Under this condition, the analytical general solutions containing free parameters are presented in this paper, which can be extended to second-order linear ordinary differential equation. These results provide valuable mathematical criteria for analyzing nonlinear phenomena in many disciplines.

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