Jordan, D.W. and Smith, P. (2007) Nonlinear Ordinary Differential Equations. Oxford University Press, Oxford, England, 1 p, 450-453, 493 p.
has been cited by the following article:
TITLE: On Two New Groups of 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.3, March 9, 2022
ABSTRACT: In this paper, we define a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We will also define a group of solutions x(t) that are equal to the amplitude. This is a generalized amplitude function. We are using Abel’s methods, described by Armitage and Eberlein. And finally, we define an exponential function whose exponent is the product of a complex number and the upper limit of integration in a non-elementary integral that can be arbitrary. At least three groups of non-elementary functions are special cases of this complex function.