  In the present paper, we present some numerical methods for computing
approximate solutions to some large differential linear matrix equations. In
the first part of this work, we deal with differential generalized Sylvester
matrix equations with full rank right-hand sides using a global Galerkin and a
norm-minimization approaches. In the second part, we consider large
differential Lyapunov matrix equations with low rank right-hand sides and use
the extended global Arnoldi process to produce low rank approximate solutions.
We give some theoretical results and present some numerical experiments.
