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