The Existence of Polynomial Solution of the Nonlinear

by Gunawan Nugroho,Totok Soehartanto,Totok R. Biyanto


Date Published: 01 Nov 2015
Published In: Information Systems International Conference (ISICO)
Volume: 2015
Publisher: Departemen Sistem Informasi, Institut Teknologi Sepuluh Nopember
Language: id-ID

Keywords: Nonlinear ordinary differential equations,the Riccati equation,analytical solutions,dynamical systems

Abstract

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.


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