Use the Laplace transform to solve the following initial value problem:

$y^{\text{'}\text{'}}-6y^{\text{'}}-27y=0,y(0)=6,y^{\text{'}}(0)=-2$

First, using $Y$ for the Laplace transform of $y(t),$ i$.$e$.,Y=L\{y(t)\},$ find the equation you get by taking the Laplace transform of the differential equation

$=0$

Now solve for $Y(s)=$ and write the above answer in its partial fraction decomposition, $Y(s)=\frac{A}{sa}\frac{B}{sb}$ where $Y(s)=y(t)=aY(s)=$

Now $by$ inverting the transform, find $y(t)=$

$$

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