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