On Solutions of Certain Non-Linear Differential-Difference Equations (2305.11234v1)

Abstract: We study about solutions of certain kind of non-linear differential difference equations $$f^{n}(z)+wf^{n-1}(z)f^{'}(z)+f^{(k)}(z+c)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z}$$ and $$f^{n}(z)+wf^{n-1}(z)f^{'}(z)+q(z)e^{Q(z)}f(z+c)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2} z},$$ where $n\geq 2$, $k\geq0$ are integers, $w, p_{1}, p_{2}, \alpha_{1}$ $&$ $\alpha_{2}$ are non-zero constants satisfying $\alpha_{1}$ $\neq$ $\alpha_{2}$, $0\not\equiv q$ is a polynomial and $Q$ is a non-constant polynomial.