Invariant algebraic curves for certain generalized Liénard differential system

In this work we solve the problem of finding invariant algebraic curves a generalized Liénard differential system $ \dot{x} = y $, \dot{y} -f(x)y-g(x) where \deg f m and g n with m+1 generalizing known previous examples. particular it is studied case 3 4 $. The difficulties in applying Puiseux method are shown even when degrees bounded.