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Mengesha, L.M. and Denekew, S.A. (2020) Revised Methods for Solving Nonlinear Second Order Differential Equations. Journal of Applied & Computational Mathematics, 9, 4.

has been cited by the following article:

• TITLE: An Attempt to Make Non-Elementary Functions That Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

  AUTHORS: Magne Stensland

  KEYWORDS: Non-Elementary Functions, Second-Order Nonlinear Autonomous ODE

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.1, January 18, 2022

  ABSTRACT: In this paper, we define an exponential function whose exponent is the product of a real number and the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of functions. Differentiating these functions twice give second-order nonlinear ODEs that have the defined set of functions as solutions.