Electron. J. Differential Equations, Vol. 2021 (2021), No. 85, pp. 1-12.

Symmetry analysis for a second-order ordinary differential equation

Sebert Feng

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.
DOI: https://doi.org/10.58997/ejde.2021.85

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Sebert Feng
The Science Academy of South Texas
Mercedes, Texas 78570, USA
email: feng14xi@gmail.com

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