Transform the differential equation

$8y^{\text{'}\text{'}\text{'}}+73y^{\text{'}\text{'}}-648y^{\text{'}}-5913y=9e^{-8t}$

$y(0)=0$

$y^{\text{'}}(0)=0$

$y^{\text{'}\text{'}}(0)=1$

into an algebraic equation by taking the Laplace transform of each side. Use $Y$ for the Laplace transform of $y,($not $Y(s)).$

Therefore

$Y=$

$=\frac{1}{s-9}+\frac{1}{s+9}+,\frac{1}{s+8}$

Taking the inverse Laplace transform we get

$y=$