8.4.1.2 Stability of the systems of equations

Problem: Investigate the stability of the system at zeroresting point. \[ \left\{\begin{array}{c} \frac{d y}{d t}=\tan ^{-1} \frac{A x}{\sqrt{1-(A x)^{2}}}+B \sin \left(\frac{\pi}{2}-y\right)-(B-y) e^{-D y} \\ \frac{d x}{d t}=C \cdot \cosh y+D \cdot \sinh (A x)-C \end{array}\right. \] \begin{tabular}{|l|l|l|l|} \hline\( A \) & \( B \) & \( C \) & \( D \) \\ \hline- & + & - & + \\ \hline \end{tabular}