2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192816In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed.16 pages, no figure, accepted in CQGGeneral Relativity and Quantum Cosmologytext