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

$y^{\text{'}\text{'}}-7y^{\text{'}}-18y=0,y(0)=-3,y^{\text{'}}(0)=4$

First, using $Y$ for the Laplace transform $ofy(t),i.e.,Y=L\{y(t)\},$

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, $Y(s)=\frac{A}{s+a}+\frac{B}{s+b}$ where

$y(t)=a$

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