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