On exponential-logarithmic solutions of linear differential systems with power series coefficients

摘要

The paper studies construction of formal exponential-logarithmic solutions for a system of ordinary linear differential equations the coefficients of which are algorithmically defined formal power series. The construction of all such solutions is generally algorithmically undecidable problem. We propose an algorithm and its implementation in Maple that make it possible to construct a basis of the space of solutions of the full-rank system if the dimension of this space is known.