  We perform an analytic investigation of the stability of line-driven disk
winds, independent of hydrodynamic simulations. Our motive is to determine
whether or not line-driven disk winds can account for the wide/broad UV
resonance absorption lines seen in cataclysmic variables (CVs) and
quasi-stellar objects (QSOs). In both CVs and QSOs observations generally
indicate that the absorption arising in the outflowing winds has a steady
velocity structure on time scales exceeding years (for CVs) and decades (for
QSOs). However, published results from hydrodynamic simulations of line-driven
disk winds are mixed, with some researchers claiming that the models are
inherently unsteady, while other models produce steady winds. The analytic
investigation presented here shows that if the accretion disk is steady, then
the line-driven disk wind emanating from it can also be steady. In particular,
we show that a gravitational force initially increasing along the wind
streamline, which is characteristic of disk winds, does not imply an unsteady
wind. The steady nature of line-driven disk winds is consistent with the 1D
streamline disk-wind models of Murray and collaborators and the 2.5D
time-dependent models of Pereyra and collaborators. This paper emphasizes the
underlying physics behind the steady nature of line-driven disk winds using
mathematically simple models that mimic the disk environment
