In this paper, we give some sufficient and necessary conditions for subordination of the solution of the Briot–Bouquet differential equation: where δ and λ are real numbers with δ≠0, δ+λ>0, and U is the unit disc in the complex plane C. Using these subordinations, we obtain some sufficient and necessary conditions that the integral operators and preserve starlikeness, where α, β, δ, and γ are real numbers with α+δ=β+γ>0, αβ≠0.