A note on the application of Darboux polynomial method to an nonlinear oscillator equation. (October 2019) - Mohanasubha, R.; Senthilvelan, M.
Abstract: In this paper, we apply Darboux polynomial method to a second-order nonlinear ordinary differential equation x ̈ + ( k 1 x q + k 2 ) x ̇ + k 3 x 2 q + 1 + k 4 x q + 1 + λ x = 0 . We identify several integrable cases in this model. We report Darboux polynomials, exponential factor and first integral for seven different choices of parameters that appear in this model. Several well known polynomial oscillator equations come out as a sub-class of the obtained results.