The Riccati Equation and the Hidden Parameter &Variable

Using suitable function transformation in combination with a specific Riccati-type equation solvable, general solution of the Riccati equation in the form of elementary quadrature is given. In the process of solving the Riccati equation, the hidden parameter and variable are discovered. This indicates that hidden parameter & variable exist in all differential equations associated with the Riccati equation, such as the second-order linear ODEs, the Schrödinger equation and the Navier–Stokes equation.

Elementary Quadrature for the Riccati equation

The authors have requested that this preprint be withdrawn due to a need to make corrections.

Elementary Quadrature for the Riccati equation

Using suitable transformation in combination with a specific Riccati-type equation solvable, the problem of solving Riccati equation can be transformed into that of a quasi-Abel equation of the second kind. By the extended Julia’s integrability condition, the general solutions of Riccati equation in the form of elementary quadrature are obtained, which contains numerous. This method opens up a new prospect for the study of nonlinear differential equations by analytical method.