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.