$(6$ marks$)$ Find the solution $to$ the following differential equation $y^{\text{'}}(t)+sin(t)y(t)=g(t)$

with the initial condition $y(0)=3on$ the interval tin$[0,2].$ The function $g(t)is$ given $by$

$g(t)=\{\begin{array}{ccc}sin(t),& if& 0t\\ -sin(t),& if& t2\end{array}$