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

TL;DR

This paper introduces a generalized Prelle-Singer method for solving third-order complex differential equations, extending techniques from real to complex domains and providing a new approach for generating integrals.

Contribution

It develops a novel generalized method for solving third-order OCDEs and introduces a new way to generate motion integrals in the complex domain.

Findings

Successfully applied the method to an example OCDE

Established a procedure for generating motion integrals in the complex domain

Extended the Prelle-Singer method from second to third order equations

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.