Algebraic and singularity properties of a class of generalisations of the Kummer-Schwarz equation (Q2186703)

The Kummer-Schwarz equation \[2y^{\prime }y^{\prime \prime \prime }-3[y^{\prime \prime }]^2=0\] is notable amongst the class of third-order ordinary differential equations due to its properties as a differential equation apart from its well-known relationship with the Schwarzian derivative. The paper under review concerns the following generalization, \[y^{(n-2)}y^{(n)}-m[y^{(n-1)}]^2=0,\] with \(m\) a parameter and \(n\geq 2\) an integer. Hence this class of equations starts at the second order. The algebraic and singularity properties as well as solutions for a number of the earlier elements of this class of differential equations are studied.