The numerical solution of the continuous-time symmetric differential matrix Riccati equations using backward differentiation formula method on the time interval \([t_{0},T_{f}] \) of the form: \(\begin{equation}\label{1} \left\{ \begin{array}{ll} \dot{X}(t)=A^TX(t)+X(t)A-X(t)BB^TX(t)+C^TC,& \hbox{} \\ X(t_{0})=X_{0}, & \end{array} \right. \end{equation}\) where \(A\in\mathbb{R}^{n\times n}\), \(B\in\mathbb{R}^{n\times s}\) and \(C\in\mathbb{R}^{p\times n}\) . Author : LAKHLIFA SADEK. E-mail: lakhlifasdek@gmail.com; sadek.l@ucd.ac.ma