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