QuestionTransform the differential equation $$\begin{array}{c} 5 y^{\prime \prime \prime}+35 y^{\prime \prime}-320 y^{\prime}-2240 y=5 e^{-6 t} \\ y(0)=0 \\ y^{\prime}(0)=0 \\ y^{\prime \prime}(0)=1 \end{array}$$ into an algebraic equation by taking the Laplace transform of each side. Use $Y$ for the Laplace transform of $y$, (not $Y(s)$ ). $$m=0$$
Therefore $$\begin{aligned} Y & =\square \\ & =\square \frac{1}{s-8}+\square \frac{1}{s+8}+\square \frac{1}{s+6} \end{aligned}$$
Taking the inverse Laplace transform we get $$y=\square$$