1 Particular Solutions of the Riccati Differential Equation with Constant Coefficients Sabit Katsayılı Riccati Diferansiyel Denkleminin Özel Çözümleri Abdullah Aydemir Mathematics Engineer and Educator Matematik Mühendisi ve Eğitimci 6.8.2025 İstanbul, Türkiye Web: http://www.abdullahaydemir.com.tr Mail: abdaydm@gmail.com Abstract In our study, we express and prove as a theorem that there exists at least one particular constant solution to the Riccati differential equation with constant coefficients. Özet Çalışmamızda sabit katsayılı Riccati diferansiyel denkleminin en az bir özel sabit çözümünün olduğunu teorem olarak ifade ediyoruz ve ispatlıyoruz. Key words: Riccati differential equation with constant coefficients, Riccati differential equation, differential equations Anahtar sözcükler: Sabit katsayılı Riccati diferansiyel denklemi, Riccati diferansiyel denklemi, diferansiyel denklemler MSC2020: 34A34, 34A05, 34-01, 34 1. Introduction In our study, we express and prove as a theorem that there exists at least one particular constant solution to the Riccati differential equation with constant coefficients. 2. Theorem and Its Proof About Particular Solutions of the Riccati Differential Equation with Constant Coefficients Theorem: Let , ,  ∈ ℝ, ≠0, ∈ℂ and  = () be given. There exists at least one particular solution of the Riccati differential equation with constant coefficients  ′ =  2 +  +  (1) such that   =  . (2)