ISOLDE --- a package for the symbolic resolution of systems of linear differential equations

We give an overview of the package ISOLDE which is implemented in the computer algebra system {\sc Maple}. It computes formal invariants, local and global (closed form) solutions of systems of linear differential equations. We then focus on the problem of computing the {\em exponential solutions} of such systems. We show how to use local information (the so-called {\em exponential parts}) in order to reconstruct global solutions. Finally, we discuss ways for an efficient computation of the exponential parts in particular without using cyclic vectors.