The dynamic magnetic properties of the mixed spin (1/2, 3/2) Ising system with bilinear nearest-neighbor exchange interactions and a crystal-field term under the presence of the external longitudinal magnetic field (ELMF) are investigated by the path probability method. First we briefly examine the equilibrium magnetic properties of the system within the cluster variation method in order to clearly understand the dynamic behavior. In particular, we investigate thermal behavior of the magnetization in detail to search whether or not the metastable and unstable branches of magnetizations occur in the system. We find that the metastable and unstable branches of magnetization only exist if the system is in the presence of the ELMF. We also presented the metastable phase diagrams in the ELMF. Then, we apply the path probability method to the system and obtain the dynamic equations. Numerical solutions of these equations are given in the form of the flow diagrams (FDs). FDs explicitly illustrate the stable, metastable and unstable states as well as the role of the unstable states and initial conditions. FDs also display how one can obtain the metastable state more easily. (C) 2020 Elsevier B.V. All rights reserved.