Elkazi, T.M. and Elkazi, S.M. (2011) On the Elkazi Transform and Ordinary Differential Equations with Variable Coefficients. Advanced in Theoretical and Applied Mathematics, 6, 13-18.

has been cited by the following article:

• TITLE: Laplace Transform, Non-Constant Coefficients Differential Equations and Applications to Riccati Equation

  AUTHORS: Malick Ndiaye

  KEYWORDS: Ordinary Differential Equations, Laplace Transform

  JOURNAL NAME: Applied Mathematics, Vol.11 No.7, July 22, 2020

  ABSTRACT: In this paper, the Laplace Transform is used to find explicit solutions of a fam-ily of second order Differential Equations with non-constant coefficients. For some of these equations, it is possible to find the solutions using standard tech-niques of solving Ordinary Differential Equations. For others, it seems to be very difficult indeed impossible to find explicit solutions using traditional methods. The Laplace transform could be an alternative way. An application on solving a Riccati Equation is given. Recall that the Riccati Equation is a non-linear differential equation that arises in many topics of Quantum Me-chanics and Physics.