Author(s)

Magne Stensland

Independent Researcher, Moldjord, Norway.

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.

Non-Elementary Functions, Second-Order Nonlinear Autonomous ODE

Stensland, M. (2022) An Attempt to Make Non-Elementary Functions That Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs. Journal of Applied Mathematics and Physics, 10, 56-67. doi: 10.4236/jamp.2022.101006.