Abstract. Solving a differential equation that contains a symbolic parameter can be seen as finding an operator that maps the parameter to the solution. Hence it is natural to develop pertinent symbolic solution algorithms on appropriate noncommutative polynomial rings that represent the relevant operators. We will show a new way to do this for the particular case of linear BVPs. A full solution algorithm will be presented, together with a pilot implementation in Theorema, a mathematical software system built on Mathematica. We will conclude by discussing various prospects of generalization.