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