On solutions of third and fourth-order time dependent Riccati equations and the generalized Chazy system

We introduce a new transformation (nonlocal) to find the general solutions of some equations belonging to the third and fourth-order time dependent Riccati class of equations. These are in turn related to the Chazy polynomial class and the time dependent F-XVI Bureau symbol PI equations respectively.

► Use of non local transformation for linearization of higher-order ordinary differential equations.
► Computation of solutions of third-order ODES using non local transformations. Application to a time-dependent Riccati chain and a generalized Chazy equation.
► Further applications of non local transformations for finding solutions of fourth-order systems in particular the time dependent fourth-order Riccati chain.