A New Method of Solving Third Order Non-Linear Ordinary Complex Differential Equation by Generalizing Prelle-Singer Method

Abstract: A new method of solving third-order ordinary complex differential equations (OCDEs) by generalizing Prelle-Singer. The idea which is a procedure for finding the solution for second-order differential equations in the real domain. We have illustrated the theory with an example. We also introduced a new way of generating second and third motion integrals in the complex domain, which is analog to motion in the real domain from the first integral and demonstrated the procedure for the method mentioned above.