Sequences of nonlinear differential equations with related solutions

Summary A second-order nonlinear differential equation which occurs (together with variants of it) in many problems of applied mathematics, physics and engineering is here reduced to a first-order equation. This equation contains a parameter which is a quadratic rational function of two parameters appearing in the original equation. By applying a certain identity for a quadratic rational function, two (finite or infinite) sequences of nonlinear differential equations are generated whose solutions are determinable whenever the solution of any equation belonging to a sequence is known. The cases amenable to exact solution by quadrature are given. Entrata in Redazione il 16 luglio 1968.