I am enjoying the commentaries from David and Carl
with analytic solutions and I liked Richard's
spreadsheet suggestion for modeling a ball drop
from 100km altitude.
For me, the spreadsheet way is effectively iterative,
and a loop in any language, can capture the velocity
profile or integrate velocity numerically for an
instantaneous altitude suitable for accessing an
analytic expression for air density and g, but without
the spreadsheet's ready plotting capability.
Matlab's solvers are in fact iterative too, and have
no problem with an initial up velocity.
See this one for example: