Analytic General Solution of the Riccati equation
Abstract
A sufficient and necessary condition for integrability of the Riccati equation, which is the simplest form of nonlinear ordinary differential equation, is established by using the elementary quadrature method. Based on this condition, the analytic general solution including free variable (parameter) and the associated entangled functions are provided, which can be extended to second-order linear ordinary differential equation. These results may provide a mathematical criterion for modern physics as well as for nonlinear phenomena in various fields.
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