I seems my question is different from this question. The version of Grönwall's inequality from wikipedia says if $u'(t) \leq \beta(t) u(t)$ then $u(t) \leq u(a) \exp(\int_{a}^t \beta(s) ds)$. Is it also true that if $u'(t) \geq \beta(t) u(t)$ then $u(t) \geq u(a) \exp(\int_{a}^t \beta(s) ds)$? It seems that the proof in Wikipedia hold with just flipping the signs. Am I correct or missing something?
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