First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation

We exploit the notion of nonholonomic transformations to deduce a time-dependent first integral for a (generalized) second-order nonautonomous Riccati differential equation. It is further shown that the method can also be used to compute the first integrals of a particular class of third-order time-dependent ordinary differential equations and is therefore quite robust.

Research highlights
► The Jacobi Last Multiplier is a useful tool for deriving the Lagrangian of such equations provided the Fels conditions are satisfied.
► Kudryashov derived two hierarchies of fourth-order ODEs which pass the Painlevé test.
► The Hamiltonization of such equations is considered using Ostrogradski’s theory.
► These contributes to the understanding of higher-order ODEs in general.