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The Kummer-Schwarz Equation, 2y'y "' - 3(y ")(2) = 0, has a generalisation, (n - 1)y((n-2))y((n)) - ny((n-1)2) - 0, which shares many properties with the parent form (see Sinuvasan R, Tamizhmani K M & Leach P G L, Algebraic and singularity properties of a class of generalisations of the Kummer-Schwarz equation differ, Equ Dyn Syst (2016), doi: 10.1007/s12591-016-0327-5) in terms of symmetry and singularity. All equations of the class are integrable in closed form. Here we introduce a new class, (n + q - 2)y((n-2))y((n)) - (n + q - 1) y((n-1)2) = 0, which has different integrability and singularity properties.

FURTHER GENERALISATIONS OF THE KUMMER-SCHWARZ EQUATION: ALGEBRAIC AND SINGULARITY PROPERTIES