Abstract
We consider the general damped nonlinear oscillator x′ = y, y′ = −a1x − a2xn+1 − a3x2n+1 − y(a4 + a5xn), where ai are real parameters for i = 1, 2, 3, 4, 5 and n is an integer. We note that these class of Liénard differential systems include a large number of physically important nonlinear oscillators. We provide a complete and rigorous characterization of these systems that admit a local analytic first integral in a neighborhood of the origin.
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