  In this paper, we consider some non-weight modules over the Lie algebra of
Weyl type. First, we determine the modules whose restriction to $U(\frak h)$
are free of rank $1$ over the Lie algebra of differential operators on the
circle. Then we determine the necessary and sufficient conditions for the
tensor products of quasi-finite highest weight modules and $U(\frak h)$-free
modules to be irreducible, and obtain that any two such tensor products are
isomorphic if and only if the corresponding highest weight modules and $U(\frak
h)$-free modules are isomorphic. Finally, we extend such results to the Lie
algebras of differential operators in the general case.
