An Easy Method For Solving nth Order Linear Ordinary Differential Equation with Variable Coefficients

Toyesh Prakash Sharma¹ , Ankush Kumar Parcha²

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.4 , pp.35-40, Aug-2023

Online published on Aug 31, 2023

Copyright © Toyesh Prakash Sharma, Ankush Kumar Parcha . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

Abstract :
With the help of this paper authors are putting forward their findings that makes un an easy method for finding solution of second order linear ordinary differential equations with variable coefficients and third-order linear ordinary differential equations with variable coefficients further applicable for nth order provided there must be some differential relation between introduced coefficients in the given differential equation then only we can solve with the help of here introduced method, the basic idea for reducing second and third order linear ordinary differential equation with variable coefficient is to use well known first order linear differential equation but of course, it limits this method and needs differentiable coefficients. In this paper authors also provide an application part that may help for understanding whether we can apply this method or not!

Key-Words / Index Term :
Differential Equations, Linear Ordinary Differential Equations, Second Order Linear Ordinary Differential Equations, Third Order Linear Ordinary Differential Equations, Variable Coefficients, First Order Linear Ordinary Differential Equation, nth Order Linear Ordinary Differential Equation.

References :
[1]. Birkhoff, G. and Rota, G.-C. (1989) Ordinary Differential Equation. 4th Edition, Wily, New York.
[2]. Adam Loverro (2004), “Fractional Calculus: History, Definitions and Applications for the Engineer”, Report, Department of Aerospace and Mechanical Engineering University of Notre Dame U.S.A. May 8, 2004.
[3]. I.Podlubny, “Riesz potential and Riemann Liouville Fractional integrals and derivatives of Jacobi polynomials”, Appl.math.lett., Vol.10, issue.1, pp.103-108. 1997.
[4]. N. H. Sweilam, et.al, Numerical Studies for Solving Fractional Riccati Differential Equation, Applications and Applied Mathematics: An International Journal (AAM), Vol. 7, Issue 2, pp. 595 – 608, 2012.
[5]. Rahmat Ali Khan, et.al “Existence And Uniqueness Of Solutions For Nonlinear Fractional Differential Equations With Integral Boundary Conditions” Fractional Differential Calculus, Volume 1, Number 1, pp. 29–43. (2011),
[6]. T. Bakkyaraj, R. Sahadevan , “An Approximate Solution To Some Classes Of Fractional Nonlinear Partial Differential-Difference Equation Using Adomian Decomposition Method”, Journal of Fractional Calculus and Applications, Vol. 5(1), pp. 37-52. (2014).
[7]. Kreider D.L., Kuller R.G., Ostberg D.R., Elementary Differential Equations, Addison-Wesley Publishing Company, Inc., Reading, MA, 1968.
[8]. Ramirez A., Takeuchi Y., Differential Equations, Limusa Publishing House, Mexico, 1975. [In Spanish].
[9]. Shohal Hossain, Samme Akter Mithy, "Methods for solving ordinary differential equations of second order with coefficients that is constant," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.9-16, 2023.
[10]. S. M. Yahya, "Solution of Second-Order Ordinary Differential Equations with Constant Coefficients," International Journal of Mathematics and Mathematical Sciences, vol. 2014, Article ID 121950, 12 pages, 2014. https://doi.org/10.1155/2014/121950.