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