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Differential equations play a prominent role in aerospace engineering by modeling aerospace structures, describing important phenomena, and simulating mathematical behavior of aerospace dynamical systems. Presently, aerospace systems have become more complex, space vehicle missions require more hours of simulation time to complete a maneuver, and high-performance missiles require more logical decisions in there phases of flight. Because of these conditions, a computationally efficient algorithm for solving these differential equations is highly demanded to significantly reduce the computing time. This paper presents an efficient method for solving the differential equations by using variational iteration method, which can be implemented into software package to dramatically reduce the computing time for simulating the aerospace systems thereby significantly improving computer's performance in real-time design and simulation of aircrafts, spacecrafts, and other aerospace vehicles.