\begin{align}
\frac{\mathrm{d} u\_{1}\left( t \right)}{\mathrm{d}t} &= p_{3} \left(  - u\_{1}\left( t \right) + u\_{2}\left( t \right) \right) \\
0 &=  - u\_{2}\left( t \right) + \frac{1}{10} \left( p_{1} - u\_{1}\left( t \right) \right) p_{2} p_{3} u\_{1}\left( t \right) \\
\frac{\mathrm{d} u\_{3}\left( t \right)}{\mathrm{d}t} &= u\_{2}\left( t \right)^{\frac{2}{3}} u\_{1}\left( t \right) - p_{3} u\_{3}\left( t \right)
\end{align}
