Exploring Vedic Sutra Techniques for Solving Ordinary Differential Equations

The primary aim of this paper is to examine the use of Vedic Mathematics sutras in deriving derivatives and solving ordinary differential equations. Vedic sutras such as Urdhva-Tiryagbhyam, Ekanyunena Purvena, Calana-Kalanabhyam, Gunakasamuccayah, and Lopanasthapanabhyam helps to simplify the computational process. The study seeks to establish the relevance and efficiency of these Vedic principles in differentiation and differential equation solving. Employing Vedic methods for obtaining derivatives and solutions significantly reduces computational complexity and enhances mental calculation speed. Some illustrative examples are presented to demonstrate the application of these sutras in differentiation. The findings indicate that Vedic Mathematics offers a simplified, faster, and more intuitive approach to solving ordinary differential equations.

Vedic Mathematics, Differential Equations, Derivatives, Urdhva-Tiryagbhyam Sutra, Calana-Kalanabhyam Sutra. Ekanyunena Purvena, Gunakasamuccayah, Lopanasthapanabhyam.

1. D. Anjali and D. B. Banswal, “Exploring the Relationship between Vedic Mathematics and Advanced Calculus,” Neuroquantology, vol. 20, pp.1336-1345, December 2022. [Google Scholar] [Crossref]

2. I. Devakumar, “Vedic Mathematics,” International Journal of Engineering Development and Research, vol. 9, pp. 123-132, 2021. [Google Scholar] [Crossref]

3. D.N. Garain and S. Kumar, “Analytical Discussion for Existence of Idea of Calculus in Vedic and Post Vedic Periods,” International Journal of Mathematics Trends and Technology, vol. 61, pp.85-88, 2018. [Google Scholar] [Crossref]

4. V.K. Gupta, “Vedic Mathematics and the Mathematics of Vedic Period– An Analysis and [Google Scholar] [Crossref]

5. Application,” 'VEDA-VIDYĀ' An International Refereed Research Journal, vol. 26, pp 193-208, December 2015. [Google Scholar] [Crossref]

6. R. Kumar, A.U. Rahman and S. Tiwari, “Integrating Vedic Mathematics with Derivatives,” [Google Scholar] [Crossref]

7. International Journal of Advance Research in Multidisciplinary, vol. 1, pp 517-521, August 2023. [Google Scholar] [Crossref]

8. P. Kumari, P Kumar and G. Rani, “Application of Vedic Formulas in Elementary Calculus,” [Google Scholar] [Crossref]

9. International Journal of Advanced Research in Science, Communication and Technology, vol. 3, pp 537-541, June 2023. [Google Scholar] [Crossref]

10. R. Kumari, “An Overview of the Ancient Indian Vedic Mathematics Techniques,” International Journal for Research in Applied Science & Engineering Technology, vol. 10, pp 1914-1919, December 2022. [Google Scholar] [Crossref]

11. R.R. Lal and D.K. Yadav, “Relevance of Vedic Mathematics Ekanyunena Purvena and Ekadhikena Purvena Sutras in Calculus,” Scope Journal, vol. 23, pp 950-957, September 2023. [Google Scholar] [Crossref]

12. A. Mandloi, “Comparative Analysis of Techniques of Vedic Mathematics,” International Journal of Mathematics Trends and Technology, vol. 68, pp 30-32, March 2022. [Google Scholar] [Crossref]

13. B.K. T. Maharaja, “Vedic Mathematics: Sixteen Simple Formulae from the Vedas,” Revised edition, Motilal Banarsidass Publisher, Delhi, 1990. [Google Scholar] [Crossref]

14. Priya, P. Goel and A. Kumar, “Vedic Mathematics in Derivatives and Integration, Differential Equations and Partial Differential Equations,” Journal of Mathematical Problems, Equations and Statistics, vol. 2, pp 27-32, June 2021. [Google Scholar] [Crossref]

15. K.K. Prasad, “An Empirical Study on Role of Vedic Mathematics in Improving the Speed of Basic Mathematical Operations,” International Journal of Management, IT and Engineering, vol. 6, pp 161 171, January 2016. [Google Scholar] [Crossref]

16. S.R. Singh and R. Yadav, “Homogenous Differential Equation Easy to Solve with Vedic Ganit,” International Vedic Mathematics Conference, 2021. [Google Scholar] [Crossref]

17. S. Vyas, “Vedic Mathematics: A Collection of Ancient Techniques to Solve Mathematical Problem in Easy and Faster Way,” International Journal of Research in all Subjects in Multilanguage, vol. 7, pp 33-38, May 2019. [Google Scholar] [Crossref]

18. A.M. Wazwaz, A First Course in Integral Equation, Second edition, World Scientific Publishing Co. Pte. Ltd., Singapore. 2015. [Google Scholar] [Crossref]

• Interplay of Students’ Emotional Intelligence and Attitude toward Mathematics on Performance in Grade 10 Algebra
• Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines
• Fixed Point Theorem in Controlled Metric Spaces
• Usage of Moving Average to Heart Rate, Blood Pressure and Blood Sugar
• Exploring Algebraic Topology and Homotopy Theory: Methods, Empirical Data, and Numerical Examples