On transcendental meromorphic solutions of certain types of differential equations

Abstract

In this paper, for a transcendental meromorphic function f and a ∈ C, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: z) , where P d (z, f ) is differential polynomial of f , p i 's and α i 's are non-vanishing rational functions and non-constant polynomials respectively. When a = 0, we have pointed out a major lacuna in a recent result of Xue [Math. Slovaca, 70(1)(2020), 87-94] and rectifying the result, presented the corrected form of the same at a large extent. The case a = 0 has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.