\frac{dx_{1}}{dt} = \left(-1 \cdot k_{23} \cdot k_{2} \cdot \left(\left(k_{17} - k_{18}\right) \cdot \exp\left(\left(-k_{19}\right) \cdot t\right) + k_{18}\right) \cdot \left(1 - k_{3}\right) \cdot x_{1} \cdot \left(x_{3} + k_{13} \cdot x_{4}\right) + -1 \cdot k_{23} \cdot \left(\left(k_{17} - k_{18}\right) \cdot \exp\left(\left(-k_{19}\right) \cdot t\right) + k_{18}\right) \cdot k_{3} \cdot \left(1 - k_{2}\right) \cdot x_{1} \cdot \left(x_{3} + k_{13} \cdot x_{4}\right) + 1 \cdot k_{23} \cdot k_{5} \cdot x_{5} + -1 \cdot k_{23} \cdot k_{2} \cdot \left(\left(k_{17} - k_{18}\right) \cdot \exp\left(\left(-k_{19}\right) \cdot t\right) + k_{18}\right) \cdot k_{3} \cdot x_{1} \cdot \left(x_{3} + k_{13} \cdot x_{4}\right)\right) / k_{23}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{23} \cdot k_{2} \cdot \left(\left(k_{17} - k_{18}\right) \cdot \exp\left(\left(-k_{19}\right) \cdot t\right) + k_{18}\right) \cdot \left(1 - k_{3}\right) \cdot x_{1} \cdot \left(x_{3} + k_{13} \cdot x_{4}\right) + -1 \cdot k_{23} \cdot k_{4} \cdot k_{6} \cdot x_{2} + -1 \cdot k_{23} \cdot k_{4} \cdot \left(1 - k_{6}\right) \cdot x_{2}\right) / k_{23}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{23} \cdot k_{4} \cdot k_{6} \cdot x_{2} + -1 \cdot k_{23} \cdot k_{22} \cdot k_{21} / \left(\left(k_{22} - k_{21}\right) \cdot \exp\left(\left(-k_{20}\right) \cdot t\right) + k_{21}\right) \cdot x_{3} + -1 \cdot k_{23} \cdot k_{9} \cdot x_{3} + -1 \cdot k_{23} \cdot k_{12} \cdot x_{3}\right) / k_{23}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{23} \cdot k_{4} \cdot \left(1 - k_{6}\right) \cdot x_{2} + -1 \cdot k_{23} \cdot k_{10} \cdot x_{4}\right) / k_{23}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{23} \cdot \left(\left(k_{17} - k_{18}\right) \cdot \exp\left(\left(-k_{19}\right) \cdot t\right) + k_{18}\right) \cdot k_{3} \cdot \left(1 - k_{2}\right) \cdot x_{1} \cdot \left(x_{3} + k_{13} \cdot x_{4}\right) + -1 \cdot k_{23} \cdot k_{5} \cdot x_{5}\right) / k_{23}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{23} \cdot k_{2} \cdot \left(\left(k_{17} - k_{18}\right) \cdot \exp\left(\left(-k_{19}\right) \cdot t\right) + k_{18}\right) \cdot k_{3} \cdot x_{1} \cdot \left(x_{3} + k_{13} \cdot x_{4}\right) + -1 \cdot k_{23} \cdot k_{8} \cdot x_{6}\right) / k_{23}\\
\frac{dx_{7}}{dt} = \left(1 \cdot k_{23} \cdot k_{22} \cdot k_{21} / \left(\left(k_{22} - k_{21}\right) \cdot \exp\left(\left(-k_{20}\right) \cdot t\right) + k_{21}\right) \cdot x_{3} + -1 \cdot k_{23} \cdot k_{11} \cdot x_{7} + -1 \cdot k_{23} \cdot k_{12} \cdot x_{7} + 1 \cdot k_{23} \cdot k_{8} \cdot x_{6}\right) / k_{23}\\
\frac{dx_{8}}{dt} = \left(1 \cdot k_{23} \cdot k_{9} \cdot x_{3} + 1 \cdot k_{23} \cdot k_{10} \cdot x_{4} + 1 \cdot k_{23} \cdot k_{11} \cdot x_{7}\right) / k_{23}