$[$Medium$]($Laplace Transform $($System$))$

Use Laplace transform method to find the PS of

$\left[\begin{array}{c}x\end{array}\right]$

$y^{\text{'}}=\left[\begin{array}{ccc}3& -1& 1\end{array}\right]$

$1\left[\begin{array}{c}x\end{array}\right]$

$y+25\left[\begin{array}{c}cost\end{array}\right]$

$sint$

$x(0)=\left[\begin{array}{c}0\end{array}\right]$

$0$