ON TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF CERTAIN TYPES OF DIFFERENTIAL EQUATIONS

In this paper, for a transcendental meromorphic function f and a is an element of 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: fn + afn-2fi + Pd(z, f) = Xk i=1 pi(z)e alpha i(z), where Pd(z, f) is a differential polynomial of f, pi's and alpha 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 [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case a =6 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.