# Cheng Equation: A Revisit Through Symmetry Analysis

## TL;DR

This paper revisits the Cheng Equation using symmetry analysis, reducing it to known forms like Abel, Riccati, and Euler equations, and discusses its general solution via Lie theory.

## Contribution

It provides a comprehensive symmetry-based analysis of the Cheng Equation, including reductions to well-known equations and the application of Lie symmetries.

## Key findings

- Reduced Cheng Equation to Abel, Riccati, and Euler equations
- Derived general solutions using Lie symmetry methods
- Extended analysis to generalized Cheng equations

## Abstract

The symmetry analysis of the Cheng Equation is performed. The Cheng Equation is reduced to a first-order equation of either Abel's Equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati Equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng Equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.