The following problem is considered: given a system of linear ordinary differential equations of arbitrary order with power series coefficients, to recognize whether it has regular solutions at point 0 and, if it does, to find them. An algorithm for solving this problem is proposed. Each power series that is a coefficient of the original system is specified by a procedure that computes the series coefficient by the index of this coefficient. The original system is assumed to have full rank; i.e., the equations of the system are independent. The algorithm is implemented in Maple.
['Sergei A. Abramov', 'D. E. Khmelnov']
Regular solutions of linear differential systems with power series coefficients