An Analytic Technique for the Solutions of Nonlinear Oscillators with Damping Using the Abel Equation

Using the Chiellini condition for integrability we derive explicit solutions for a generalized system of Riccati equations ẍ + αx 2n+1 ẋ + x 4n+3 = 0 by reduction to the firstorder Abel equation assuming the parameter α ≥ 2 2(n + 1).The technique, which was proposed by Harko et al, involves use of an auxiliary system of first-order differential equations sharing a common solution with the Abel equation.In the process analytical proofs of some of the conjectures made earlier on the basis of numerical investigations in [25] is provided.