Chapter 5.4, Problem 25P

Use the Laplace transform to solve the system

$x\text{'}\text{'}-y\text{'}\text{'}+x-4y=0,x\text{'}+y\text{'}=\cos t$,

$x\left(0\right)=0,x\text{'}\left(0\right)=0,y\left(0\right)=0,y\text{'}\left(0\right)=1$