This paper shows that explicit and exact general periodic solutions for various types of Lienard equations can be computed by applying the generalized Sundman transformation. As an il- lustration of the efficiency of the proposed theory, the cubic Duffing equation and Painleve- Gambier equations were considered. As a major result, it has been found, for the first time, that equation XII of the Painleve-Gambier classication can exhibit, according to an appropriate parametric choice, trigonometric solutions, but with a shift factor.
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