\frac{dx_{1}}{dt} = \left(1 \cdot k_{1} \cdot \left(10 \cdot k_{2} - x_{1}\right) / \left(1 + k_{2} + x_{1} + x_{2}^{2}\right) + -1 \cdot k_{1} \cdot \left(2 \cdot x_{1} - x_{2}\right) / \left(1 + x_{1} + x_{2}\right)\right) / k_{1}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{1} \cdot \left(2 \cdot x_{1} - x_{2}\right) / \left(1 + x_{1} + x_{2}\right) + -1 \cdot k_{1} \cdot \left(x_{2} - x_{3}\right) / \left(1 + x_{2} + x_{3} + x_{4}^{2}\right) + -1 \cdot k_{1} \cdot \left(x_{2} - x_{5}\right) / \left(1 + x_{2} + x_{5} + x_{6}^{2}\right)\right) / k_{1}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{1} \cdot \left(x_{2} - x_{3}\right) / \left(1 + x_{2} + x_{3} + x_{4}^{2}\right) + -1 \cdot k_{1} \cdot \left(5 \cdot x_{3} - x_{4}\right) / \left(1 + x_{3} + x_{4}\right)\right) / k_{1}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{1} \cdot \left(5 \cdot x_{3} - x_{4}\right) / \left(1 + x_{3} + x_{4}\right) + -1 \cdot k_{1} \cdot \left(10 \cdot x_{4} - k_{3}\right) / \left(1 + x_{4} + k_{3}\right)\right) / k_{1}\\
\frac{dx_{5}}{dt} = \left(1 \cdot k_{1} \cdot \left(x_{2} - x_{5}\right) / \left(1 + x_{2} + x_{5} + x_{6}^{2}\right) + -1 \cdot k_{1} \cdot \left(5 \cdot x_{5} - x_{6}\right) / \left(1 + x_{5} + x_{6}\right)\right) / k_{1}\\
\frac{dx_{6}}{dt} = \left(1 \cdot k_{1} \cdot \left(5 \cdot x_{5} - x_{6}\right) / \left(1 + x_{5} + x_{6}\right) + -1 \cdot k_{1} \cdot \left(10 \cdot x_{6} - k_{4}\right) / \left(1 + x_{6} + k_{4}\right)\right) / k_{1}\\
\frac{dx_{7}}{dt} = 0\\
\frac{dx_{8}}{dt} = 0\\
\frac{dx_{9}}{dt} = 0