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 x+αx²ⁿ⁺¹ x˙+x⁴ⁿ⁺³ = 0 by reduction to the first-order Abel equation assuming the parameter 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 [1] is provided.