8.4.1.5 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: \[ \left\{\begin{array}{l} \frac{d y}{d t}=\operatorname{sh}(A x)+\frac{\pi}{2} \operatorname{sh}(B y) \\ \frac{d x}{d t}=\cos \left(\frac{\pi}{2} x\right)+c e^{y}-D \sec y \end{array}\right. \] \begin{tabular}{|l|l|l|l|} \( A \) & \( B \) & \( C \) & \( D \) \\ \hline- & - & - & - \end{tabular}