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