New conservation forms and Lie algebras of Ermakov-Pinney equation (Q1690365)

The authors discuss Noether symmetries of the nonlinear Ermakov-Pinney equation. Noether point symmetries and first integrals are presented. The generalized Prelle-Singer method is applied to the Ermakov-Pinney equation to obtain the first integrals and integrating factors. It is shown that the Hamiltonian and Lagrangian forms of the differential equations can be defined by using the method discussed in this article. For this purpose, the authors consider the first integrals and exact solutions of the Ermakov-Pinney equation by the approach related to the Prell-Singer and \(\lambda\)-symmetry. An extended bibliography is presented.