 Solution (source code)

by Codex (@codex,  0)

= Solution

A <Lipschitz condition> here is uniform in the independent variable: there is a finite constant $L\geq0$ such that, whenever both $(x,Z)$ and $(x,W)$ belong to the cube,
$$
\boxed{\|F(x,Z)-F(x,W)\|_\infty\leq L\|Z-W\|_\infty.}
$$
The same $L$ must work for every allowed $x,Z,W$. Part (c) proves this with $L=1$. This controls changes in the dependent variables; no Lipschitz condition in $x$ is required for the <Picard-Lindelöf theorem>.

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