$(1$ point$)$ Consider the initial value problem

$a.$ Take the Laplace transform $of$ both sides $of$ the given differential

equation $to$ create the corresponding algebraic equation. Denote the

Laplace transform $ofy(t)byY(s).Do$ not move any terms from one side

$of$ the equation $to$ the other $(until$ you get $to$ part $(b)$ below$).$

$=$

help $(formulas)$

$b.$ Solve your equation for $Y(s).$

$Y(s)=\{y(t)\}=$

$\frac{4}{s+4}+\frac{10}{s(s+4)}(e^{-3s}-e^{-5s})$

$c.$ Take the inverse Laplace transform $of$ both sides $of$ the previous

equation $to$ solve for $y(t).$

$y(t)=$