Entire solutions of certain type binomial differential equations (Q2684881)

In this paper, the authors studied the complex differential equation \[ f'f''-af^2=be^{2c}, \] where \(a,b,c\) are polynomials such that \(ab\not\equiv0\) and \(c\) is non-constant. In fact, they provided all possibilities of the entire solutions \(f\) of the above differential equations under the conditions that \(f\) is an entire function and all zeros of \(f'\) are simple.