Abstract
The Ermakov-Pinney equation possesses three Lie point symmetries with the algebra sl(2, R).This algebra does not provide a representation of the complete symmetry group of the Ermakov-Pinney equation.We show how the representation of the group can be obtained with the use of the method described in Nucci, J. Nonlin.Math.Phys.12 (2005) (this issue), which is based on the properties of Jacobi's last multiplier (Bianchi L, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni, Enrico Spoerri, Pisa, 1918), the method of reduction of order (Nucci,J.Math.Phys 37 (1996), 1772-1775) and an interactive code for calculating symmetries (Nucci, Interactive REDUCE programs for calcuating classical, non-classical and Lie-Bäcklund symmetries for differential equations (preprint: Georgia Institute of Technology, Math 062090-051, 1990, and CRC Handbook of Lie Group Analysis of Differential Equations.