Exact Periodic Solutions of Truly Nonlinear Oscillator Equations and Quadratic Liénard-Type Equations

The present research contribution is devoted to solving the integrability problem of Lienard type differential equations. It is shown that such a problem may be solved by nonlocal transformation for some classes of equations. By doing so, it is observed that the integrability of a class of restricted Duffing type equations with integral power or fractional power nonlinearity may be secured by that of a general class of quadratic Lienard type differential equation, and vice versa. Such a restricted Duffing type equation is also shown to be closely related to a quadratic Lienard type equation for which exact and explicit general solution may be computed. In this context it has been shown that exact and general periodic solutions may be computed for these two classes of restricted Duffing equations and quadratic Lienard type equations. The comparison of obtained solutions with some well-known results is carried out in some cases.