After the initial seminal works of Sophus Lie on ordinary differential equations, several
important results on point symmetry group analysis of ordinary differential equations have …

Nonlinear ordinary differential equations: A discussion on symmetries and singularities Page 1
International Journal of Geometric Methods in Modern Physics Vol. 13, No. 7 (2016) 1630009 …

A method for finding general solutions of second-order nonlinear ordinary differential
equations by extending the Prelle–Singer (PS) method is briefly discussed. We explore …

The existence of a Lagrangian description for the second-order Riccati equation is analyzed
and the results are applied to the study of two different nonlinear systems both related with …

A Liénard type nonlinear oscillator of the form x ̈+ kxx ̇+(k 2∕ 9) x 3+ λ 1 x= 0, which may
also be considered as a generalized Emden-type equation, is shown to possess unusual …

In this paper, we consider a generalized second-order nonlinear ordinary differential
equation (ODE) of the form x ̈+(k 1 x q+ k 2) x ̇+ k 3 x 2 q+ 1+ k 4 x q+ 1+ λ 1 x= 0⁠, where …

For general values of the parameter, k, the equation y"+ yy'+ ky 3= 0 can be reduced to
quadrature via a Lie algebraic approach, either direct or through hidden symmetries. For …

In a previous paper (see [10]) we established the form of second-order ordinary differential
equations with two commuting symmetries (in canonical form G1=∂/∂, G2=∂/∂ q, G2≠ p …

A periodically forced Liénard system is capable of generating frequent large-amplitude
chaotic bursts for a range of system and external forcing parameter values which are known …

In this paper, we show that the force-free Duffing–van der Pol oscillator is completely
integrable for a specific parametric choice. We derive a general solution for this parametric …