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