Entire solutions of certain type of differential equations II

We analyze the transcendental entire solutions of the following type of nonlinear differential equations: f n ( z ) + P ( f ) = p 1 e α 1 z + p 2 e α 2 z in the complex plane, where p 1 , p 2 and α 1 , α 2 are nonzero constants, and P ( f ) denotes a differential polynomial in f of degree at most n − 1 with small functions of f as the coefficients.