  We consider an evolution of anisotropic cosmological model on the example of
the Bianchi type I homogeneous universe. It is filled by the mixture of matter
and dark energy with an arbitrary barotropic equation of state (EoS). The
general solution for this case is found and analyzed. A complete list of
possible future singularities for this model is given. Some new solution were
obtained for a particular EoSs, e.g. for the Bianchi type I {\Lambda}CDM
homogeneous model. It is shown that all special cases corresponding to
different EoSs have common properties, provided that now or at another moment
of time the Universe is expanding, and the density of the mixture is positive.
Then the evolution always begins with an anisotropic "Big Bang" which happened
a finite time ago. After that the universe is constantly expanding and, in all
cases, with rare exceptions, becomes more isotropic. A particularly strong
isotropization is associated with the epoch of inflation. After its completion,
the expansion of the universe becomes almost isotropic, and this case cannot be
distinguished from isotropic by astronomical observations. This fact allows us
to consider an anisotropic cosmological model as a possible candidate for the
description of the observed Universe despite the isotropic pattern of
expansion.
