College of Education for Pure Sciences, University of Mosul discussed a master dissertation on solving ODE systems using particle swarm optimization and genetic algorithm based on Padé approximant by the postgraduate student, Mrs. Reham Haitham Salim Al-Azzawi. The dissertation highlighted that the transformation of systems of ordinary differential equations into constrained optimization problems to find approximate solutions to them, because many solutions of systems of linear and nonlinear ODEs contain different formulas, so Padé approximant expansion was used, which is a fractional expansion to obtain High accuracy results compared to other enlargements. The dissertation demonstrated that the application of the two algorithms (the swarm algorithm and the genetic algorithm) to a group of ODE systems. It was found that the two algorithms are convergent and gave accurate results in most of the tests and that these results demonstrate the ability of the proposed algorithm to solve linear and nonlinear ODE systems with initial or boundary conditions.