Consider the following ODE:
$$\frac{\text{d}}{\text{d}t} \binom{x}{y} = A\binom{x}{y} + \binom{0}{x g(t)}$$
- $A$ is a constant;
- $g(t)$ is a bounded function, and all its derivatives are bounded;
- Solutions of $\frac{\text{d}}{\text{d}t} \binom{x}{y} = A\binom{x}{y}$ are bounded $\forall t$;
Is there a simple/effective way (without solving it) to prove that the solutions remain bounded as $t\to+\infty$?