In past work, an analytic solution of the Boltzmann transform as a function of matric potential was proposed to estimate the soil water content profile for horizontal water infiltration into porous media. However, it could only be successfully described for sands, but with singularity at position x = 0. Later, others introduced the concept of air-entry pressure to divide the soil water retention curve into saturated and unsaturated domains to provide an exact solution of the Bruce and Klute equation, with no restrictions, while assuming the initial soil water content to be zero before the infiltration process. The problem remained that the above-mentioned analytical solution was limited to sands, while the Bruce- and Klute-based approach was limited to zero water content at the beginning. This study was based on both previous studies, and the objective was to develop a solution that works for all soil types and does not depend on zero initial soil moisture content. As a result, an alternative solution is presented that generalizes the centenary theory of Green and Ampt for any homogeneous soil.