On the integrability of Lienard I-type equations via lambda-symmetries and solvable structures

摘要

For Lienard I-type equations it is proved the existence of a family of lambda-symmetries such that any of them lets the computation by quadratures of a time-dependent first integral of the equation. This is achieved by using a solvable structure constructed out of the lambda-symmetry and one Lie point symmetry. The first integral obtained by quadratures and the first integral associated to the Lie symmetry generator are always functionally independent and they can be therefore used to integrate completely the Lienard I-type equation.