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In [1,2] we have developed a method (we call it the S-function method) thatis successful in treating certain classes of rational second order ordinarydifferential equations (rational 2ODEs) that are particularly `resistant' tocanonical Lie methods and to Darbouxian approaches. In this present paper, wegeneralize the S-function method making it capable of dealing with a class ofelementary 2ODEs presenting elementary functions. Then, we apply this method toa Duffing-Van der Pol forced oscillator, obtaining an entire class of firstintegrals.

A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator