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The Li\'enard equation is used in various applications. Therefore,constructing general analytical solutions of this equation is an importantproblem. Here we study connections between the Li\'enard equation and someequations from the Painlev\'e--Gambier classification. We show that with thehelp of such connections one can construct general analytical solutions of theLi\'enard equation's subfamilies. In particular, we find three new integrablefamilies of the Li\'enard equation. We also propose and discuss an approach forfinding one--parameter families of closed--form analytical solutions of theLi\'enard equation.

On connections of the Li\'enard equation with some equations of Painlev\'e--Gambier type