A search for solutions of linear differential systems of an arbitrary order with formal power series coefficients

We investigate problems of the construction of Lorent, regular and exponentially-logarithmic solutions of linear differential systems of full rank. We assume that the system coefficients are formal power series defined algorithmically. A system may have an arbitrary order. It is shown that the first two problems are solvable algorithmically, and the third is not. We give a simplified version of the third porblem which is algorithmically solvable: if a given system $S$ and a non-negative integer $d$ are such that for $S$ one has $d$ linear independent solutions, then we can construct them algorithmically.