= Solution
The <characteristic equations for a quasilinear equation> here are
$$
x_s=1,\qquad y_s=z,\qquad z_s=2.
$$
Successive integration gives the general characteristic
$$
\boxed{x=s+a,\qquad z=2s+c,\qquad y=s^2+cs+b,}
$$
where $a,b,c$ are integration constants. Equivalently $z-2x$ and $y-z^2/4$ are constant along each curve: differentiating them with respect to $s$ gives zero. Three constants occur because shifting the origin of the parameter $s$ describes the same geometric curve again; there are two independent curve invariants.
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