\frac{dx_{1}}{dt} = \left(1 \cdot k_{13} \cdot k_{8} \cdot x_{1} \cdot \ln\left(k_{7} / x_{1}\right) + -1 \cdot k_{13} \cdot k_{10} \cdot x_{3} \cdot x_{1} + -1 \cdot k_{13} \cdot k_{9} \cdot x_{1}\right) / k_{13}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{13} \cdot k_{1} \cdot k_{14} + -1 \cdot k_{13} \cdot k_{2} \cdot x_{2} + -1 \cdot k_{13} \cdot k_{11} \cdot x_{2} \cdot x_{1} / \left(x_{1} + k_{12}\right)\right) / k_{13}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{13} \cdot k_{4} \cdot x_{3} \cdot x_{1} / \left(x_{1} + k_{12}\right) + -1 \cdot k_{13} \cdot k_{5} \cdot x_{3} + -1 \cdot k_{13} \cdot k_{6} \cdot x_{1} \cdot x_{3} + 1 \cdot k_{13} \cdot k_{3} \cdot k_{11} \cdot x_{2} \cdot x_{1} / \left(x_{1} + k_{12}\right)\right) / k_{13}\\
\frac{dx_{4}}{dt} = 0\\
\frac{dx_{5}}{dt} = 0