This paper presents a solution to the differential equation of longitudinal dispersion in porous media without using the coordinate transformation (x - ut), which leads to an asymmetrical concentration distribution. The solution is derived under the assumption that the porous medium is homogeneous and isotropic, with no mass transfer between the solid and liquid phases. The governing equation is derived based on mass conservation and is given by: $$ D\nabla^{2}C=u\frac{\partial C}{\partial x}+\frac{\partial C}{\partial t} $$ where D is the dispersion coefficient, C is the concentration of the solute, u is the average velocity, and t is time. The solution is applied to a semi-infinite medium with a plane source at x=0, and the boundary conditions are C(0,t)=C₀, C(x,0)=0, and C(∞,t)=0. The solution is obtained by transforming the equation and applying the Laplace transform, leading to an expression involving the error function. The solution is expressed as: $$ \frac{C}{C_{0}}=\frac{1}{2}\left[\mathrm{erfc}\left(\frac{1-\xi}{2\sqrt{\xi\eta}}\right)+e^{\frac{u x}{D}}\mathrm{erfc}\left(\frac{1+\xi}{2\sqrt{\xi\eta}}\right)\right] $$ where ξ = ut/x and η = D/ux. The first term in the solution corresponds to a symmetrical concentration distribution, while the second term accounts for asymmetry. The paper shows that for small values of η, the second term becomes negligible, and the solution approaches the symmetrical case. Experimental results support this conclusion, indicating that the concentration distribution is approximately symmetrical for values of x chosen some distance from the source. The paper also discusses the error introduced by neglecting the second term of the solution. It is shown that for η < 0.002, the error introduced by neglecting the second term is less than 3%. The paper concludes that the solution is not symmetrical about x = ut for large values of η, but experimental evidence suggests that D is small, leading to an approximately symmetrical concentration distribution. Theoretical results indicate that the concentration distribution approaches a symmetrical case as η approaches zero, with errors of the order of experimental errors.This paper presents a solution to the differential equation of longitudinal dispersion in porous media without using the coordinate transformation (x - ut), which leads to an asymmetrical concentration distribution. The solution is derived under the assumption that the porous medium is homogeneous and isotropic, with no mass transfer between the solid and liquid phases. The governing equation is derived based on mass conservation and is given by: $$ D\nabla^{2}C=u\frac{\partial C}{\partial x}+\frac{\partial C}{\partial t} $$ where D is the dispersion coefficient, C is the concentration of the solute, u is the average velocity, and t is time. The solution is applied to a semi-infinite medium with a plane source at x=0, and the boundary conditions are C(0,t)=C₀, C(x,0)=0, and C(∞,t)=0. The solution is obtained by transforming the equation and applying the Laplace transform, leading to an expression involving the error function. The solution is expressed as: $$ \frac{C}{C_{0}}=\frac{1}{2}\left[\mathrm{erfc}\left(\frac{1-\xi}{2\sqrt{\xi\eta}}\right)+e^{\frac{u x}{D}}\mathrm{erfc}\left(\frac{1+\xi}{2\sqrt{\xi\eta}}\right)\right] $$ where ξ = ut/x and η = D/ux. The first term in the solution corresponds to a symmetrical concentration distribution, while the second term accounts for asymmetry. The paper shows that for small values of η, the second term becomes negligible, and the solution approaches the symmetrical case. Experimental results support this conclusion, indicating that the concentration distribution is approximately symmetrical for values of x chosen some distance from the source. The paper also discusses the error introduced by neglecting the second term of the solution. It is shown that for η < 0.002, the error introduced by neglecting the second term is less than 3%. The paper concludes that the solution is not symmetrical about x = ut for large values of η, but experimental evidence suggests that D is small, leading to an approximately symmetrical concentration distribution. Theoretical results indicate that the concentration distribution approaches a symmetrical case as η approaches zero, with errors of the order of experimental errors.