A$.12$ Solve the initial$-$value problem for the following system of first$-$order differential equations:

$\frac{d{x}_1}{dt}=-2x_1+2x_2+f(t)$

$\frac{d{x}_2}{dt}=x_1-3x_2$

$x_1(0)=x_2(0)=0$

where $f(t)$ is a given function.