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: fⁿ+afⁿ⁻²f'+ P_d(z,f) = ∑_i=1^kp_i(z)e^α_i(z), where Pd(z,f)
Nearby in the stack
is differential polynomial of
f
,
pi
's and
αi
'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.
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