Article citationsMore>>

Salas, A.H., Jairo, E. and Castillo, H. (2014) Exact Solution to Duffing Equation and the Pendulum Equation. Applied Mathematical Sciences, 8, 8781-8789.
https://doi.org/10.12988/ams.2014.44243

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.