This paper is on the optimization and control of renewable energy systems (RES) orchestrated by associated characteristics like variability and intermittency of renewable resources like solar or wind. These challenges are solved in this study by formulating a differential equation model for the optimal dynamic RES. It contains the main components, energy input, storage capacity, and output requirement, and mathematical techniques like outcome-optimum and genetic algorithms that convey gradient. Some samples of challenging situations that were imposed on the model include severe dynamic loading, step-by-step tests, and dynamic perturbations on the outputs that helps to approve the performance and stability of the proposed model achieved by MATLAB and Simulink tools. The results however preliminary only show that the model boosts predictability as well as reliability in how energy is produced to match consumption patterns and minimize wastage. The results imply the necessity of the rapid and flexible approaches use in the context of renewable. With the model in mind which takes into consideration the interaction of the identified variables, differential equation resolves the challenges of energy resources management for enhanced environmental and economic performances. Otherwise, there are some recommendations for further studies: expanding the usage of the developed model to other dynamic systems as smart grids, water resources, and etc., further development of integration of artificial intelligence to increase the efficiency of real-time decisions making. This research opens avenues for further improvements in the application of renewable energy especially in the management aspect as shown by the significant contribution of mathematical modeling in the efficient deployment of renewable energy.