This paper presents a solution to the differential equation governing longitudinal dispersion in porous media, avoiding the use of the coordinate transformation $(x - ut)$ and symmetrical boundary conditions. The authors derive a solution that results in an asymmetrical concentration distribution, which approaches symmetry when the dispersion coefficient $D$ is small and the region near the source is not considered. The solution is obtained using Duhamel's theorem and Laplace transforms, and it is shown that for large values of $\eta = D / u x$, the concentration distribution becomes significantly asymmetrical. Experimental results support the theoretical findings, indicating that for distances greater than 10 cm or 350 cm from the source, the concentration distribution is approximately symmetrical. The paper concludes that while the solution is asymmetrical for large $\eta$, it is only necessary to consider the first term of the solution for practical applications, as the second term introduces errors within the range of experimental uncertainties.This paper presents a solution to the differential equation governing longitudinal dispersion in porous media, avoiding the use of the coordinate transformation $(x - ut)$ and symmetrical boundary conditions. The authors derive a solution that results in an asymmetrical concentration distribution, which approaches symmetry when the dispersion coefficient $D$ is small and the region near the source is not considered. The solution is obtained using Duhamel's theorem and Laplace transforms, and it is shown that for large values of $\eta = D / u x$, the concentration distribution becomes significantly asymmetrical. Experimental results support the theoretical findings, indicating that for distances greater than 10 cm or 350 cm from the source, the concentration distribution is approximately symmetrical. The paper concludes that while the solution is asymmetrical for large $\eta$, it is only necessary to consider the first term of the solution for practical applications, as the second term introduces errors within the range of experimental uncertainties.