\[ \left \{x'(t)+x(t)-y'(t)=2 t,x''(t)-9 x(t)+y'(t)+3 y(t)=\sin (2 t)\right \} \] ✓ Mathematica : cpu = 0.666614 (sec), leaf count = 170
\[\left \{\left \{x(t)\to \frac {1}{16} e^{-3 t} \left (e^{4 t} \left (c_1 (20 t+7)+c_2 (4 t+3)+3 c_3 (1-4 t)\right )+9 c_1-3 \left (c_2+c_3\right )+32 e^{3 t} (t+2)\right )-\frac {36}{325} \sin (2 t)-\frac {2}{325} \cos (2 t),y(t)\to \frac {1}{8} e^{-3 t} \left (e^{4 t} \left (c_1 (20 t-3)+4 c_2 t-12 c_3 t+c_2+9 c_3\right )+3 c_1-c_2-c_3+16 e^{3 t} (3 t+5)\right )-\frac {37}{325} \sin (2 t)+\frac {16}{325} \cos (2 t)\right \}\right \}\]
✓ Maple : cpu = 0.106 (sec), leaf count = 80
\[ \left \{ \left \{ x \left ( t \right ) =-{\frac {2\,\cos \left ( 2\,t \right ) }{325}}+4-{\frac {36\,\sin \left ( 2\,t \right ) }{325}}+2\,t+{\it \_C1}\,{{\rm e}^{t}}+{\it \_C2}\,{{\rm e}^{-3\,t}}+{\it \_C3}\,{{\rm e}^{t}}t,y \left ( t \right ) ={\frac {16\,\cos \left ( 2\,t \right ) }{325}}-{\frac {37\,\sin \left ( 2\,t \right ) }{325}}+2\,{\it \_C1}\,{{\rm e}^{t}}+{\frac {2\,{\it \_C2}\,{{\rm e}^{-3\,t}}}{3}}+2\,{\it \_C3}\,{{\rm e}^{t}}t-{\it \_C3}\,{{\rm e}^{t}}+10+6\,t \right \} \right \} \]