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On Solutions of Certain Non-Linear Differential-Difference Equations

Authors:
Garima Pant at University of Delhi
Garima Pant
Sanjay Kumar at Deen Dayal Upadhyaya College (University of Delhi)
Sanjay Kumar
  • Deen Dayal Upadhyaya College (University of Delhi)
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Abstract

We study about solutions of certain kind of non-linear differential difference equations fn(z)+wfn−1(z)f′(z)+f(k)(z+c)=p1eα1z+p2eα2zf^{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 fn(z)+wfn−1(z)f′(z)+q(z)eQ(z)f(z+c)=p1eα1z+p2eα2z,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≥2n\geq 2, k≥0k\geq0 are integers, w,p1,p2,α1w, p_{1}, p_{2}, \alpha_{1} &\& α2\alpha_{2} are non-zero constants satisfying α1\alpha_{1} ≠\neq α2\alpha_{2}, 0≢q0\not\equiv q is a polynomial and Q is a non-constant polynomial.

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