I have this (decoupled) BVP (where $\lambda <0$):
$y_1'(t) = \lambda y_1(t) \\ y_2'(t) = - \lambda y_2(t) \\ y_1(0) = 1, \quad y_2(a)=1$
for $t \in [0,a]$. It has been written in the notes that the BVP is stable since the solution $y_1(t) = e^{\lambda t}, y_2(t) =e^{a \lambda } e^{-\lambda t} $ remains bounded for $t \to \infty$.
I want to know how is $y_2(t)$ bounded as $t \to \infty$.