Entire solutions of certain type of differential equations II

We analyze the transcendental entire solutions of the following type of nonlinear differential equations: fn(z)+P(f)=p1eα1z+p2eα2z in the complex plane, where p1, p2 and α1, α2 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.