\frac{dx_{1}}{dt} = \left(-1 \cdot k_{13} \cdot k_{5} \cdot x_{1} + -1 \cdot k_{13} \cdot k_{11} \cdot k_{10} \cdot x_{3} \cdot x_{1} + 1 \cdot k_{13} \cdot k_{11} \cdot x_{2} \cdot x_{3} \cdot x_{1}\right) / k_{13}\\
\frac{dx_{2}}{dt} = \left(-1 \cdot k_{13} \cdot k_{2} \cdot x_{2} + -1 \cdot k_{13} \cdot \operatorname{piecewise}(1, t < 1, \operatorname{piecewise}(1, t > 15, \frac{21}{5000})) \cdot k_{8} \cdot x_{2} \cdot x_{3} + 1 \cdot k_{13} \cdot k_{1}\right) / k_{13}\\
\frac{dx_{3}}{dt} = \left(-1 \cdot k_{13} \cdot k_{3} \cdot x_{3} + 1 \cdot k_{13} \cdot \operatorname{piecewise}(1, t < 1, \operatorname{piecewise}(1, t > 15, \frac{21}{5000})) \cdot k_{8} \cdot x_{2} \cdot x_{3} + -1 \cdot k_{13} \cdot k_{9} \cdot x_{3} \cdot x_{4}\right) / k_{13}\\
\frac{dx_{4}}{dt} = \left(-1 \cdot k_{13} \cdot k_{7} \cdot x_{4} + 1 \cdot k_{13} \cdot k_{11} \cdot k_{10} \cdot x_{3} \cdot x_{1}\right) / k_{13}