Use Laplace transforms to convert the following nonhomogeneous systems of differential equations into an algebraic system, and find the solutions of the differential equations.

a.

\[\begin{aligned} x^{\prime} & =2 x+3 y+2 \sin 2 t, \quad x(0)=1 \\ y^{\prime} & =-3 x+2 y, \quad y(0)=0 \end{aligned}\]

b.

\[\begin{array}{ll} x^{\prime}=-4 x-y+e^{-t}, & x(0)=2 \\ y^{\prime}=x-2 y+2 e^{-3 t}, & y(0)=-1 \end{array}\]

c.

\[\begin{array}{ll} x^{\prime}=x-y+2 \cos t, & x(0)=3 \\ y^{\prime}=x+y-3 \sin t, & y(0)=2 \end{array}\]