In this paper, we study main headlines of brain development which is a major problem in neurobiology in present. Our aim here is to find the analytical solution of the equation that belongs to the brain development system. For this solution, the exchange of cerebellum granule cells in EGL (External granule layer of the cerebellum) is discussed. For this reason, Lie symmetry analysis is used. Obtaining solutions of this system means determining the behavior of the granular cell numbers at different stages. Knowing the behavior of these cells provides important information about the progression and development of diseases. Examples of these diseases are abnormal cerebellum development, cerebellum cancer. In this study, time dependent probability function related to division of two granule cells is examined. Then, analytical solutions are obtained for three different states of this function. Some tables and density graphics of these solutions are given.