Considering the system:
\begin{equation} \begin{cases} \dv{x}{t} = -2x+y+(1-\sigma)z \\ \dv{y}{t} = 3x-y \\ \dv{z}{t} = (3-\sigma y)x-z\\ \end{cases} \end{equation}
with the initial locations \((x_0, y_0, z_0)= (-1,1,2)\).
We notice first that the top and bottom expressions as a factor in \(x\) multiplied by \(y\), which means that our system is not homogenous. Let’s expand all the expressions first.
\begin{equation} \begin{cases} \dv{x}{t} = -2x+y+(1-\sigma)z \\ \dv{y}{t} = 3x-y \\ \dv{z}{t} = 3x-\sigma yx-z\\ \end{cases} \end{equation}