Symmetry and singularity properties of second-order ordinary differential equations of Lie's Type III.
The canonical equation of Type III in Lie's classification of scalar second-order ordinary differential equations is studied from the viewpoint of it being linearizable and possessing the Painlevé property. It is shown that there is a wider class of equations than the so-called modified Painlevé Ince equation, which is of Type III, that can be linearized via nonlocal transformations. In this class, a relationship between the parameters of the singularity analysis and the structure of the reduced equation is found.
scientific article; zbMATH DE number 5123999