Nonlocal Transformation of Ermakov-Pinney Equation

In this study, we will examine nonlocal transformation which is calledSundman transformation. Firstly, the Ermakov-Pinney equation isclassified by special functions to apply this transformation. After thisclassification, the class of equations is determined and the suitabletransformation for this class will be chosen. Sundman transformationpair will be obtained by using an appropriate method. Moreover, thefirst integrals of the Ermakov-Pinney equation are found by thistransformation pair.

Keywords:

Nonlocal transformation pair , Differential equations , First Integral , Ermakov-Pinney Equation