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