I am looking to show that if y(t) is continuous on (a, b) and satisfies

$$y(t)\leq H+K\int_{t}^{t_{0}} y(s)ds,\quad\forall\ a<t\leq t_0$$

where $t_0 \in (a,b)$, then

$$y(t)\leq He^{K(t_0-t)},\quad\forall\ a<t\leq t_0$$

  • $\begingroup$ Do you want $h(s)$ and not $y(s)$ under your integral sign? $\endgroup$ – Robert Lewis Oct 22 '18 at 22:55
  • $\begingroup$ In this case what is the function $h$ ? $\endgroup$ – Delta-u Oct 23 '18 at 13:20
  • $\begingroup$ That is a great question. Perhaps that is the trouble with it. Let's suppose that was a mistake. I will change the question to represent that. $\endgroup$ – Sekkou527 Oct 23 '18 at 15:07

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