### First integrals of reducible completely solvable systems of equations in total differentials

Title First integrals of reducible completely solvable systems of equations in total differentials A. F. Pranevich11Yanka Kupala State University of Grodno We consider reducible (with respect to various transformation groups) completely solvable system of linear homogeneous equations in total differentials. The spectral method of building first integrals for this differential system is elaborated. The method is based on the existence of linear partial integral (real, complex-valued or multiple) for reducible differential system. This partial integral is constructed by the common eigenvectors and eigenvalues of the matrices of reducible differential system. In addition, in this article some examples are given to illustrate the obtained results. reducible system of equations in total differentials, condition of complete solvability, partial integral, first integral Pranevich A. F. ''First integrals of reducible completely solvable systems of equations in total differentials'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 141-152. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper20.pdf. - Date of access: 15.08.2022.