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We study the problem of solvability of linear differential systems with smallcoefficients in the Liouvillian sense (or, by generalized quadratures). For ageneral system, this problem is equivalent to that of solvability of the Liealgebra of the differential Galois group of the system. However, dependence ofthis Lie algebra on the system coefficients remains unknown. We show that forthe particular class of systems with non-resonant irregular singular pointsthat have sufficiently small coefficient matrices, the problem is reduced tothat of solvability of the explicit Lie algebra generated by the coefficientmatrices. This extends the corresponding Ilyashenko-Khovanskii theorem obtainedfor linear differential systems with Fuchsian singular points. We also givesome examples illustrating the practical verification of the presented criteriaof solvability by using general procedures implemented in Maple.

Linear Differential Systems with Small Coefficients: Various Types of Solvability and their Verification