\frac{dx_{1}}{dt} = \left(1 \cdot k_{12} \cdot k_{1} + 1 \cdot k_{12} \cdot k_{2} \cdot k_{13} + -1 \cdot k_{12} \cdot k_{3} \cdot x_{1} + -1 \cdot k_{12} \cdot k_{4} \cdot x_{1} \cdot x_{4}\right) / k_{12}\\
\frac{dx_{2}}{dt} = 0