  This study deals with the Ulam stability of non-autonomous linear
differential systems without assuming the condition that they admit an
exponential dichotomy. In particular, the best (minimal) Ulam constants for
two-dimensional non-autonomous linear differential systems with generalized
Jordan normal forms are derived. The obtained results are applicable not only
to systems with solutions that exist globally on $(-\infty,\infty)$, but also
to systems with solutions that blow up in finite time. New results are included
even for constant coefficients. A wealth of examples are presented, and
approximations of node, saddle, and focus are proposed. In addition, this is
the first study to derive the best Ulam constants for non-autonomous systems
other than periodic systems.
