We aim to solve the (almost) simplest possible differential equation problem

$$\begin{align} u'(t) &= -au(t) \tag{1}\\ u(0) &= I \tag{2} \end{align}$$ Here, $t\in (0,T]$ $a$, $I$, and $T$ are prescribed parameters $u(t)$ is the unknown function The ODE (1) has the initial condition (2)