Trigonometric Identities and Entire Solutions of Non-linear Binomial Differential Equations

Using Nevanlinna's value distribution theory of meromorphic functions, we study the entire solutions of non-linear binomial differential equations with linkages to trigonometric identities. We also investigate the growth of entire solutions of non-linear monomial differential-difference equations. Some results obtained generalize the previous results given by Gundersen et al. (J Math Anal Appl 507:125788, 2022). Furthermore, we propose some problems about this family of non-linear binomial differential equations in the end of this paper.