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The Duffing equation describes the oscillations of a damped nonlinear oscillator . Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited e.g. oscillations of a theoretical weightless-spring. We propose generalizing the mathematical features of the Duffing equation by including in addition to the cubic term unlimited number of odd powers of coordinate-dependent terms. The proposed generalization describes a truedoi:10.4236/jemaa.2011.35022 fatcat:5rg2yuy6tbeula4tmiq3vplxf4