Chandrasakar, V.K., Senthilvelan, M. and Lakshmanan, M. (2008) On the Complete Integrability and Linearization of Nonlinear Ordinary Differential Equations. Proceedings of the RoyaL Society A, 461.
https://doi.org/10.1098/rspa.2008.0240

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.