Chapter 8 - Linear Differential Equations of Order n - 8.10 Chapter Review - Additional Problems - Page 575: 14

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Given $F(x)=5e^{-x}+4x$ Since, $D^2$ is the annihilator of $G(x)=4x$ Also, we have: $(D+1)$ is the annihilator of $H(x)=e^{-x}$.This implies that the $(D+1)$ is the annihilator of $5H(x)=5e^{-x}$ So, $F(x)=5H(x)+G(x)$ Therefore, $(D+1)D^2$ is the annihilator of F(x).