Systems of matrix linear differential equations of first order

Sufficient conditions for the solvability in quadratures of systems of matrix linear ordinary differential equations of first order with one-sided multiplication by variable matrix coefficients are given in this paper. These conditions are stated in terms of the theory of Lie algebras. We consider matrix equations of higher orders that are equivalent to such systems. An illustrative example is considered. Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 63–75, July, 1999.