  In this article we give a characterization of left (right) quasi-duo
differential polynomial rings. In particular, we show that a differential
polynomial ring is left quasi-duo if and only if it is right quasi-duo. This
yields a partial answer to a question posed by Lam and Dugas in 2005. We
provide non-trivial examples of such rings and give a complete description of
the maximal ideals of an arbitrary quasi-duo differential polynomial ring.
Moreover, we show that there is no left (right) quasi-duo differential
polynomial ring in several indeterminates.
