Chapter 8 - Linear Differential Equations of Order n - 8.3 The Method of Undetermined Coefficients: Annihilators - Problems - Page 525: 1

$D+3$ is the annihilator of $F(x)$,

We consider the function $F(x)=5e^{-3x}$ We are given that $D+3$ is the annihilator of $G(x)=e^{-3x}$ This implies that the $F(x)=5 G(x)$ Therefore, $D+3$ is the annihilator of $F(x)$,