  We use Wetterich's parameterization equation of state (EOS) of dark energy to
a $5D$ Ricci-flat cosmological solution and we suppose the universe contains
three major components: matter, radiation and dark energy. By using the
relation between the scale factor and the redshift $z$, we show that the two
arbitrary functions contained in the $5D$ solution could be solved out
analytically in terms of the variable $z$. Thus the whole $5D$ solution could
be constructed uniquely if the current values of the three density parameters
$\Omega_{m0}$, ${\Omega_{r0}}$, $\Omega_{x0}$, the EOS $w_{0}$%, and the
bending parameter $b$ contained in the EOS are all known. Furthermore, we find
that all the evolutions of the mass density $\Omega_{m} $, the radiation
density ${\Omega_{r}}$, the dark energy density $\Omega_{x}$, and the
deceleration parameter $q$ depend on the bending parameter $b$ sensitively.
Therefore it is deserved to study observational constraints on the bending
parameter $b$.
