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Duarte, L.G.S., Duarte, S.E.S., da Mota, L.A.C.P. and Skea, J.E.F. (2000) Solving Second-Order Ordinary Differential Equations by Extending the Prelle-Singer Method. Journal of Physics A: Mathematical and General, 34, 3015.
https://doi.org/10.1088/0305-4470/34/14/308

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.