\frac{dx_{1}}{dt} = \left(-1\right) \cdot k_{1} \cdot k_{2} \cdot \left(x_{1} - x_{2}\right) / \operatorname{piecewise}(500, t \le k_{12}, 400)\\
\frac{dx_{2}}{dt} = \left(k_{1} \cdot k_{2} \cdot \left(x_{1} - x_{2}\right) - k_{1} \cdot k_{2} \cdot \left(x_{2} - x_{3}\right) - k_{3} \cdot x_{2} \cdot \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100}) - k_{4} \cdot x_{2} \cdot \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100})\right) / \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100})\\
\frac{dx_{3}}{dt} = \left(k_{1} \cdot k_{2} \cdot \left(x_{2} - x_{3}\right) - k_{7} \cdot x_{3} \cdot \operatorname{piecewise}(380, t \le k_{12}, 280) - k_{11} \cdot x_{3} \cdot \operatorname{piecewise}(380, t \le k_{12}, 280)\right) / \operatorname{piecewise}(380, t \le k_{12}, 280)\\
\frac{dx_{4}}{dt} = \left(-1\right) \cdot k_{9} \cdot k_{2} \cdot \left(x_{4} - x_{5}\right) / \operatorname{piecewise}(500, t \le k_{12}, 400)\\
\frac{dx_{5}}{dt} = \left(k_{9} \cdot k_{2} \cdot \left(x_{4} - x_{5}\right) - k_{9} \cdot k_{2} \cdot \left(x_{5} - x_{6}\right) + k_{3} \cdot x_{2} \cdot \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100})\right) / \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100})\\
\frac{dx_{6}}{dt} = \left(k_{9} \cdot k_{2} \cdot \left(x_{5} - x_{6}\right) + k_{7} \cdot x_{3} \cdot \operatorname{piecewise}(380, t \le k_{12}, 280)\right) / \operatorname{piecewise}(380, t \le k_{12}, 280)\\
\frac{dx_{7}}{dt} = \left(-1\right) \cdot k_{10} \cdot k_{2} \cdot \left(x_{7} - x_{8}\right) / \operatorname{piecewise}(500, t \le k_{12}, 400)\\
\frac{dx_{8}}{dt} = \left(k_{10} \cdot k_{2} \cdot \left(x_{7} - x_{8}\right) - k_{10} \cdot k_{2} \cdot \left(x_{8} - x_{9}\right) + k_{4} \cdot x_{2} \cdot \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100})\right) / \operatorname{piecewise}(\frac{33}{100}, t \le k_{12}, \frac{33}{100})\\
\frac{dx_{9}}{dt} = \left(k_{10} \cdot k_{2} \cdot \left(x_{8} - x_{9}\right) + k_{11} \cdot x_{3} \cdot \operatorname{piecewise}(380, t \le k_{12}, 280)\right) / \operatorname{piecewise}(380, t \le k_{12}, 280)