On Solutions of Certain Non-Linear Differential-Difference Equations

Abstract

We study about solutions of certain kind of non-linear differential difference equations $$f^n(z)+w{f}^{n-1}(z)f^{{}^{\prime }}(z)+f^{(k)}(z+c)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z}$$ and $$f^n(z)+w{f}^{n-1}(z)f^{{}^{\prime }}(z)+q(z)e^{Q(z)}f(z+c)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z},$$ where $n\ge 2$, $k\ge 0$ are integers, $w,p_1,p_2,{\alpha }_1$ $\&$ ${\alpha }_2$ are non-zero constants satisfying ${\alpha }_1$ $\ne$ ${\alpha }_2$, $0\not\equiv q$ is a polynomial and $Q$ is a non-constant polynomial.