$In$ this exercise $we$ will use the Laplace transform $to$ solve the following initial value problem:

$y^{\text{'}}+4y=\{\begin{array}{cc}-4,& 0t<mn>1</mn>\\ 0,& 1t\\ y(0)=-1\end{array}$

$(1)$ First, using $Y$ for the Laplace transform $ofy(t),i.e.,Y=L(y(t)),$ find the equation obtained $by$ taking the

Laplace transform $of$ the initial value problem