Haynes Christensen

09/09/2023 · Primary School

Use the annihilator method to determine the form of a particular solution for the given equation. \( \mathrm{y}^{\prime \prime}+16 \mathrm{y}^{\prime}+65 \mathrm{y}=2 e^{-8 \mathrm{x}} \cos \mathrm{x}+\mathrm{x} \) Find a differential operator that will annihilate the nonhomogeneity \( 2 e^{-8 \mathrm{x}} \cos \mathrm{x}+\mathrm{x} \). \( \mathrm{D}^{2}\left(\mathrm{D}^{2}+16 \mathrm{D}+65\right) \) (Type the lowest-order annihilator that contains the minimum number of terms. Type your answer in factored or expanded form. What is the form of the particular solution? \( \mathrm{y}_{\mathrm{p}}(\mathrm{x})=\square \)