\frac{dx_{1}}{dt} = -1 \cdot k_{18} \cdot k_{1} \cdot \left(1 - k_{12}\right) \cdot \left(1 - k_{13}\right) \cdot \left(k_{11} \cdot x_{3} + x_{4}\right) / \left(x_{8} - x_{5}\right) \cdot x_{1} / k_{18}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{18} \cdot k_{1} \cdot \left(1 - k_{12}\right) \cdot \left(1 - k_{13}\right) \cdot \left(k_{11} \cdot x_{3} + x_{4}\right) / \left(x_{8} - x_{5}\right) \cdot x_{1} + -1 \cdot k_{18} \cdot k_{9} \cdot \left(1 - k_{10}\right) \cdot x_{2} + -1 \cdot k_{18} \cdot k_{9} \cdot k_{10} \cdot x_{2}\right) / k_{18}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{18} \cdot k_{9} \cdot k_{10} \cdot x_{2} + -1 \cdot k_{18} \cdot k_{6} \cdot x_{3} + -1 \cdot k_{18} \cdot k_{2} \cdot x_{3}\right) / k_{18}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{18} \cdot k_{9} \cdot \left(1 - k_{10}\right) \cdot x_{2} + -1 \cdot k_{18} \cdot k_{5} \cdot x_{4} + -1 \cdot k_{18} \cdot k_{3} \cdot x_{4} + -1 \cdot k_{18} \cdot k_{7} \cdot x_{4}\right) / k_{18}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{18} \cdot k_{5} \cdot x_{4} + 1 \cdot k_{18} \cdot k_{6} \cdot x_{3} + -1 \cdot k_{18} \cdot k_{4} \cdot x_{5} + -1 \cdot k_{18} \cdot k_{8} \cdot x_{5}\right) / k_{18}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{18} \cdot k_{3} \cdot x_{4} + 1 \cdot k_{18} \cdot k_{2} \cdot x_{3} + 1 \cdot k_{18} \cdot k_{4} \cdot x_{5}\right) / k_{18}\\
\frac{dx_{7}}{dt} = \left(1 \cdot k_{18} \cdot k_{7} \cdot x_{4} + 1 \cdot k_{18} \cdot k_{8} \cdot x_{5}\right) / k_{18}\\
\frac{dx_{9}}{dt} = \left(1 \cdot k_{18} \cdot k_{5} \cdot x_{4} + 1 \cdot k_{18} \cdot k_{6} \cdot x_{3}\right) / k_{18}