Article citationsMore>>

Panayotounakos, D.E. and Zampoutis, T.I. (2011) Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs. International Journal of Mathematics and Mathematical Sciences, 2011, Article ID: 387429.
https://doi.org/10.1155/2011/387429

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.