  We present a method for solving the two-dimensional linearized collisionless
Boltzmann equation using Fourier expansion along the orbits. It resembles very
much solutions present in the literature, but it differs by the fact that
everything is performed in coordinate space instead of using action-angle
variables. We show that this approach, though less elegant, is both feasible
and straightforward. This approach is then incorporated in a matrix method in
order to calculate self-consistent modes, using a set of potential-density
pairs which is obtained numerically. We investigated the stability of some
unperturbed disks having an almost flat rotation curve, an exponential disk and
a non-zero velocity dispersion. The influence of the velocity dispersion, halo
mass and anisotropy on the stability is further discussed.
