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\begin{equation*}
  \begin{aligned}
  \frac{dv_1}{dt} &= \frac{R_4}{R_1 R_3 C_1} v_2 + 
    \frac{1}{R_{11} C_1} v_1 (v_0^2 - v_1^2 - \frac{v_2^2}{\alpha^2}), \\
 \frac{dv_2}{dt} &= -\frac{1}{R_2 C_2} v_1 + 
   \frac{1}{R_{22} C_2} v_2 (v_0^2 - v_1^2 - \frac{v_2^2}{\alpha^2}).
  \end{aligned}
\end{equation*}
\end{document}