Neural Ordinary Differential Equations (NODE) have emerged as a novel approach to deep learning, where instead of specifying a discrete sequence of hidden layers, it parameterizes the derivative of the hidden state using a neural network. The solution to the underlying dynamical system is a flow, and various papers have explored the universality of flows, in the senseof being able to approximate any analytical function.In this paper we present preliminary work aimed at identifying families of systems of ordinary differential equations (SODE) that are universal, in the sense that they encompass most of the systems of differential equations that appear in practice. Once one of these (candidate) universal SODEs is found, we define a process that generates a family of NODEs whose flows are precisely the solutions of this universal SODE. We present three candidates for universal SODE family: the generalized Lotka-Volterra families of differential equations; the Riccati dynamical systems; and the S-systems.We present the NODE models built upon each one of these dynamical systems and a description of their appropriate flows together with some preliminary implementations of these processes and results on learning some analytical functions.