An Attempt to Make Non-Elementary Functions That Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define an exponential function whose exponent is the product of a real number and upper limit integration in non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage Eberlein. The key to start with function, differentiating inverting, then set functions. Differentiating these functions twice give second-order nonlinear ODEs have defined as solutions.