Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 85, pp. 1-12.

Title: Symmetry analysis for a second-order ordinary differential equation
       
Author: Sebert Feng (The Science Academy of South Texas, Mercedes, TX, USA)

Abstract:
 In this article, we apply the Lie symmetry analysis to a second-order nonlinear
 ordinary differential equation, which is a Lienard-type equation with quadratic
 friction. We find the infinitesimal generators under certain parametric conditions
 and apply them to construct canonical variables.
 Also we present some formulas for the first integral for this equation.

Submitted January 18, 2021. Published October 15, 2021.
Math Subject Classifications: 34A05, 34L30.
Key Words: Lie symmetry; Lienard equation; infinitesimal generator;
      second-order ordinary differential equation; harmonic oscillator.