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