A Simplified and innovative solution to the exact differential equation and its comparison with the method of Arfken and koshlyakov

This research introduces a simplified boundary-fixing method for solving first-order exact differential equations, which reduces computational complexity while maintaining accuracy. The proposed approach is compared with classical techniques, particularly those developed by George B .Arfken and Nikolai G. koshlyakov, with both theoretical and pratical examples provided to demonstrate its efficacy . Through these comparisons, the paper aims to show the advantages of the new method in terms of computational efficiency and ease of application. KEYWORDS : Differential Equation , solving , Arfken , theoretical , Koshlyakov , accurate