Meromorphic solution of a class of non-linear differential equations with sharing one value

Abstract

Here we report the finding of the meromorphic solution of a general differential equation which is in the form $$G^{(i)}=\sum _{k=0}^{j}c_{k}G^{k},$$ where $$c_{0}, c_{1}, \ldots ,c_{j} \not \equiv 0 $$ are small functions of G. The results concerning Linear, Riccati, Abel, Bernoulli, Ginzburg–Landau and Jacobi elliptic differential equations are obtained as special ones of the present study. Differential equations with transcendental nonlinearity are shown to be also covered by the present general study.