Using Laplace, $(1)$ solve the following differential equation with zero initial conditions by hand, and then $(2)$ use MATLAB to solve them:

$x^{}(t)+2x^{}(t)+5x(t)=sin(2t),$ where $x(0)=0$ and $x^{}(0)=0.$

$y^{}(t)-3y^{}(t)+2y(t)=e^{3t}sin(4t),$ where $y(0)=1$ and $y^{}(0)=0.$

$z^{}(t)+4z^{}(t)+3z(t)=t^{2}cos(3t),$ where $z(0)=2$ and $z^{}(0)=-1.$

$w^{}(t)+6w^{}(t)+8w(t)=t^3{e}^{2t},$ where $w(0)=-1$ and $w^{}(0)=2.$

$u^{}(t)+2u^{}(t)+10u(t)=cos(3t),$ where $u(0)=3$ and $u^{}(0)=1.$