Comparative Evaluation of Conventional Calculus Methods and Vedic Approaches in Solving Differential Equations

Abstract

The present paper focuses on the structural applicability of some computational principles of Vedic Mathematics by Bharati Krishna Tirthaji [8] to the algebraic transformation techniques used in solving ordinary differential equations. The present work does not aim to replace the traditional calculus techniques used for solving differential equations by proposing an alternative approach based on Vedic Mathematics. It aims to establish the conceptual correspondence between the traditional solution techniques and the principles of Vedic Mathematics while solving ordinary differential equations. Some typical first-order ordinary differential equations, which are separable, homogeneous, linear, and exact types of equations, are solved by traditional calculus techniques and Vedic Mathematics principles of algebraic transformation logic. The findings of the present work reveal that although the results are identical from an analytical point of view, there exist some structural similarities between the algebraic transformation techniques used by Vedic Mathematics and the traditional calculus techniques while solving the mentioned types of equations by applying the principles of Parāvartya Yojayet [5], Anurūpyena [4], Vilokanam [9], Sankalana-Vyavakalanabhyam [1], and Urdhva-Tiryagbhyam [2]. It is concluded that Vedic computational philosophy may act as an alternative theoretical approach to higher-level mathematical analysis.