2019/09/11 by Swarup Poria, Poria, Swarup, Aman Dhiman +1
Mathematics · #Chaotic Dynamics (nlin.CD) #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #History and Overview (math.HO) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1909.04916
openalex publication_date 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The method of variation of parameter (VOP) for solving linear ordinary differential equation is revisited in this article. Historically, Lagrange and Euler explained the method of variation of parameter in the context of perturbation method. In this article, we explain the construction of particular solutions of a linear ordinary differential equation in the light of linearly independent functions in a more systematic way. In addition, we have shown that if the time variation of the constants contribute substantially to the velocity then also the solution remains invariant. VOP method for system of n linear ODE is discussed. Duhamels principle has also been studied in reference to a system of n linear ODE for completeness of this review. Finally, applications of VOP method for constructing Green's function is reported.