\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +2\,y \left ( t \right ) =3\,t,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) -2\,x \left ( t \right ) =4 \right \} } \]
Mathematica: cpu = 0.027003 (sec), leaf count = 132 \[ \left \{\left \{x(t)\to -c_2 \sin (2 t)+c_1 \cos (2 t)+\cos (2 t) \left (\frac {3}{2} t \sin (2 t)-\frac {5}{4} \cos (2 t)\right )-\sin (2 t) \left (\frac {5}{4} \sin (2 t)+\frac {3}{2} t \cos (2 t)\right ),y(t)\to c_1 \sin (2 t)+c_2 \cos (2 t)+\cos (2 t) \left (\frac {5}{4} \sin (2 t)+\frac {3}{2} t \cos (2 t)\right )+\sin (2 t) \left (\frac {3}{2} t \sin (2 t)-\frac {5}{4} \cos (2 t)\right )\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 39 \[ \left \{ \left \{ x \left ( t \right ) =\sin \left ( 2\,t \right ) {\it \_C2}+\cos \left ( 2\,t \right ) {\it \_C1}-{\frac {5}{4}},y \left ( t \right ) =-\cos \left ( 2\,t \right ) {\it \_C2}+\sin \left ( 2\,t \right ) {\it \_C1}+{\frac {3\,t}{2}} \right \} \right \} \]