Please answer it all poooo. I just bafldly needed it huhu. promise i will give u a thumbs up

Coursework $2$:

I. Find the Laplace transform of the following equations:

$g(t)=\{\begin{array}{c}0\\ t-3& \text{f}\text{o}\text{r}& 05\end{array}f(t)=e^{-2t}si{n}^2(t)f(t)=cos(at+b)y^{\text{'}\text{'}}(t)+y^{\text{'}}(t)-2y(t)=-4$;$y(0)=2$;$y^{\text{'}}(0)=3x^{\text{'}\text{'}}(t)+x^{\text{'}}(t)=4e^t$;$x(0)=1$;$x^{\text{'}}(0)=3y^{\text{'}\text{'}}+4y=sint,y(0)=2,y^{\text{'}}(0)=2Y(s)=-S^2(S+3{)}^2$