TITLE:
Four New Examples of the Non-Elementary Expo-Elliptic 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.4,
April
28,
2022
ABSTRACT: In this paper, we define four new examples of the non-elementary expo-elliptic functions. This is 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. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles, and systems of nonlinear ODEs that these functions are giving solutions to.