Keywords: Nonlinear ordinary differential equations,the Riccati equation,analytical solutions,dynamical systems
The method to solve the nonlinear differential equation with variable coefficients is presented in this work. The method is based on the application of general Riccati equation, which is substituted into the considered nonlinear equation and produce polynomial equation. The polynomial order higher than four is reduced into the fourth order and solved by radicals. The solutions of the Riccati and polynomial are then combined performing the complete solution which is smooth for all time.