A slightly less general version of this question was asked, in a subsequent comment, by the OP of the question at Controlling subsolutions of a second order linear ODE Let $ f:[0,\infty) \to \mathbb{R}$ obey the differential inequality \begin{equation} f” – 2a f’ + (a^2+b^2) f \le 0,\tag{*} \end{equation} where $ a\in\mathbb R$ and $Read more