8.4.1.3 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. \[ \left\{\begin{array}{c} \frac{d y}{d t}=A \sin y+C x e^{-\frac{B}{D} x} \\ \frac{d x}{d t}=B \sinh (A x)+D \tan (C y) \end{array}\right. \] \begin{tabular}{|c|c|c|c|} \hline\( A \) & \( B \) & \( C \) & \( D \) \\ \hline+ & + & - & - \\ \hline \end{tabular}