\frac{dx_{1}}{dt} = k_{1} - k_{6} \cdot x_{1} \cdot x_{3} - k_{2} \cdot x_{1} + \left(k_{5} + k_{8}\right) \cdot x_{4}\\
\frac{dx_{2}}{dt} = k_{3} \cdot x_{1}^{2} - k_{7} \cdot x_{2}\\
\frac{dx_{3}}{dt} = k_{4} \cdot x_{2} - k_{6} \cdot x_{1} \cdot x_{3} + \left(k_{5} + k_{9}\right) \cdot x_{4} - k_{8} \cdot x_{3}\\
\frac{dx_{4}}{dt} = k_{6} \cdot x_{1} \cdot x_{3} - \left(k_{5} + k_{9}\right) \cdot x_{4} - k_{8} \cdot x_{4}