In this paper, we consider the differential equation $$F^{prime}-Q_1=Re^{alpha}(F-Q_2)$$, where $Q_1$ and $Q_2$ are polynomials with $Q_1Q_2{ eq}0$, R is a rational function and ${alpha}$ is an entire function. We consider solutions of the form $F=f^n$, where f is an entire function and $n{geq}2$ is an integer, and we prove that if f is a transcendental entire function, then $frac{Q_1}{Q_2}$ is a polynomial and $f^{prime}=frac{Q_1}{nQ_2}f$. This theorem improves some known results and answers an open question raised in [16].