Use Lemma 2.7 (Generalized Gronwall's inequality) to show that if function $\psi(t)$ satisfies
$\psi(t) \le a + \int_0^t (\beta \psi(s) + \gamma) ds$, for $t \in [0, T]$,
for given constants $a, \gamma \in \mathbb{R}, \beta > 0$, then
$\psi(t) \le ae^{\beta t} + \frac{\gamma}{\beta}(e^{\beta t} - 1)$, for $t \in [0, T]$.
Hint: Introduce the function $\tilde{\psi}(t) = \psi(t) + \frac{\gamma}{\beta}$.
