The author considers the th-order linear homogeneous differential equation
in the neighborhood of infinity, where , , are analytic at infinity. Formal solutions to (1) are given by
with . The author restricts his attention to the case in which the are distinct. From the ’s the author classifies explicit solutions and implicit solutions. Here, asymptotic properties of both solutions are discussed. One of the main results is that explicit solutions can be defined uniquely by their asymptotic behavior along a single ray.