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)