Cheng equation: A revisit through symmetry analysis

Abstract

The symmetry analysis of the Cheng equation is performed. The Cheng equation is reduced to a rst-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.

Key words: Symmetry analysis, reduction of order, closed-form solution.