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