  The Drazin inverse solutions of the matrix equations ${\rm {\bf A}}{\rm {\bf
X}} = {\rm {\bf B}}$, ${\rm {\bf X}}{\rm {\bf A}} = {\rm {\bf B}}$ and ${\rm
{\bf A}}{\rm {\bf X}}{\rm {\bf B}} ={\rm {\bf D}} $ are considered in this
paper. We use both the determinantal representations of the Drazin inverse
obtained earlier by the author and in the paper. We get analogs of the Cramer
rule for the Drazin inverse solutions of these matrix equations and using their
for determinantal representations of solutions of some differential matrix
equations, ${\bf X}'+ {\bf A}{\bf X}={\bf B}$ and ${\bf X}'+{\bf X}{\bf A}={\bf
B}$, where the matrix ${\bf A}$ is singular.
