  We construct new classes of cosmological solution to the five dimensional
Einstein-Maxwell-dilaton theory, that are non-stationary and almost conformally
regular everywhere. The base geometry for the solutions is the four-dimensional
Bianchi type IX geometry. In the theory, the dilaton field is coupled to the
electromagnetic field and the cosmological constant term, with two different
coupling constants. We consider all possible solutions with different values of
the coupling constants, where the cosmological constant takes any positive,
negative or zero values. In the ansatzes for the metric, dilaton and
electromagnetic fields, we consider dependence on time and two spatial
directions. We also consider a special case of the Bianchi type IX geometry, in
which the geometry reduces to that of Eguchi-Hanson type II geometry and find a
more general solution to the theory.
