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

$y^{\text{'}\text{'}}+-4y^{\text{'}}+4y=0,y(0)=-7,y^{\text{'}}(0)=2$

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, $Y(s)=\frac{A}{s+a}+\frac{B}{(s+a{)}^2}$

$Y(s)=,+$

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