\frac{dx_{1}}{dt} = \left(1 \cdot k_{9} \cdot x_{2} / k_{9} + -1 \cdot k_{9} \cdot k_{1} \cdot x_{1} / k_{9}\right) / k_{9}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{9} \cdot k_{5} \cdot \operatorname{piecewise}(\sin\left(t\right)^{2}, t < k_{7} \cdot \pi, 0) \cdot \operatorname{piecewise}(1, t < k_{8}, 0) / k_{9} + 1 \cdot k_{9} \cdot k_{2} \cdot x_{3}^{2} / \left(k_{6}^{2} + x_{3}^{2}\right) / k_{9} + -1 \cdot k_{9} \cdot x_{2} / k_{9}\right) / k_{9}\\
\frac{dx_{3}}{dt} = \left(1 \cdot k_{9} \cdot k_{1} \cdot x_{1} / k_{9} + -1 \cdot k_{9} \cdot k_{2} \cdot x_{3} / k_{9} + -1 \cdot k_{9} \cdot k_{3} \cdot x_{4} \cdot x_{3} / k_{9}\right) / k_{9}\\
\frac{dx_{4}}{dt} = \left(1 \cdot k_{9} \cdot x_{2} / k_{9} + -1 \cdot k_{9} \cdot k_{4} \cdot x_{4} / k_{9}\right) / k_{9}