  The basic models of modern cosmology work in FRW spacetime. Hence follows
that it is important to study the physical and mathematical nature of FRW
cosmological models. In this work, we consider FRW models with the differential
equations of state. Some new classes integrable and nonintegrable FRW
cosmological models were constructed. It is remarkable that all proposed
integrable and nonintegrable FRW models admit exact solutions. For some of
them, such exact solutions are presented. Some artificial two-dimensional FRW
models were also proposed. Finally in Appendix, we extend the obtained results
for g-essence models and for its two reductions: k-essence and f-essence.
