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In this letter we show that the force-free Duffing-van der Pol oscillator iscompletely integrable for a specific parametric choice. We derive a generalsolution for this parametric choice. Further, we describe a procedure toconstruct the transformation which removes the time dependent part from thefirst integral and provide the general solution by quadrature. The procedure isshown to have a wider applicability through additional examples. We also showthat through our method one can deduce linearizing transformations in a simpleand straightforward way and illustrate it with a specific example.Comment: 8 pages, 1 figure, J. Phys. A: Math. Gen. 37 (2004) to appea

New aspects of integrability of force-free Duffing–van der Pol oscillator and related nonlinear systems