On the generalizations of the Kummer–Schwarz equation

We carry out complete group classifications of two non-homogeneous generalizations of the Kummer–Schwarz equation. In particular we prove that the symmetry algebra for one of them is sl(2,R)⊕sl(2,R) and that it can be mapped by an equivalence transformation to the homogeneous Kummer–Schwarz equation. For this purpose we calculate the continuous equivalence group for that equation. We also study the linearization of the considered equations19