EDB — 1R7

[1R7]Let \(U⊆ ℝ^ 2\) be open, let \(f,g:U→ℝ\) be continuous with \(f≥ g\); let \(I⊆ℝ\) be an open interval with \(t_ 0∈ I\), and let \(x,w:I→ℝ\) solutions of

with \(x(t_ 0)≥ w(t_ 0)\): then \(x(t)≥ w(t)\) for \(t≥ t_ 0\). Note indeed that \(x'(t)≥ w'(t)\) and therefore \(x(t)-w(t)\) is an increasing function.