8.4.1.7 Stability of the systems of equations

Problem: Find the resting points (equilibrium) of the system and investigate the stability of the system at these points: \[ \left\{\begin{array}{l} \frac{d y}{d t}=C \cdot \arcsin \frac{B x}{\sqrt{1+(B x)^{2}}}+A \tan (D y) \\ \frac{d x}{d t}=A \cdot \operatorname{th}(B y)+D \cdot x e^{-\frac{C}{D} x} \end{array}\right. \] \begin{tabular}{|l|l|l|l|} \hline\( A \) & \( B \) & \( C \) & \( D \) \\ \hline- & + & - & + \\ \hline \end{tabular}