  We consider a cosmological model of the late universe constituted by standard
cold dark matter plus a dark energy component with constant equation of state w
and constant effective speed of sound. Neglecting fluctuations in the dark
energy component we obtain an equation describing the evolution of sub-horizon
cold dark matter perturbations through the epoch of dark matter-dark energy
equality. We explore its analytic solutions and calculate an exact w-dependent
correction for the dark matter growth function, logarithmic growth function and
growth index parameter through the epoch considered. We test our analytic
approximation with the numerical solution and find that the discrepancy is less
than 1% for k =0 in the epoch of interest.
