EDB — 1QK

[1QK]Prerequisites:[1QH]↺↻.

Describe all the differentiable functions \(f:ℝ→ℝ\) that solve

Show that if \(-1{\lt}f(x){\lt}1\) for \(x∈ I\) open interval, then \(f\) is a sine arc, for \(x∈ I\).

Show that all solutions are \(C^ 1\), and that they are piecewise \(C^∞\).

Note that \(f≡ 1\) and \(f≡ -1\) are envelopes of the other solutions, as explained in the section [1QB]↺↻.