\[ \left \{x''(t)+6 x(t)+7 y(t)=0,3 x(t)+y''(t)+2 y(t)=2 t\right \} \] ✓ Mathematica : cpu = 0.572168 (sec), leaf count = 200
\[\left \{\left \{x(t)\to \frac {1}{180} e^{-t} \left (27 c_1 e^{2 t}+27 c_2 e^{2 t}-63 c_3 e^{2 t}-63 c_4 e^{2 t}+42 \left (c_2+c_4\right ) e^t \sin (3 t)+126 \left (c_1+c_3\right ) e^t \cos (3 t)+27 c_1-27 c_2-63 c_3+63 c_4+280 e^t t\right ),y(t)\to \frac {1}{60} e^{-t} \left (-9 c_1 e^{2 t}-9 c_2 e^{2 t}+21 c_3 e^{2 t}+21 c_4 e^{2 t}+6 \left (c_2+c_4\right ) e^t \sin (3 t)+18 \left (c_1+c_3\right ) e^t \cos (3 t)-9 c_1+9 c_2+21 c_3-21 c_4-80 e^t t\right )\right \}\right \}\]
✓ Maple : cpu = 0.054 (sec), leaf count = 64
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {14\,t}{9}}+{\it \_C1}\,{{\rm e}^{t}}+{\it \_C2}\,\cos \left ( 3\,t \right ) +{\it \_C3}\,{{\rm e}^{-t}}+{\it \_C4}\,\sin \left ( 3\,t \right ) ,y \left ( t \right ) =-{\it \_C1}\,{{\rm e}^{t}}+{\frac {3\,{\it \_C2}\,\cos \left ( 3\,t \right ) }{7}}-{\it \_C3}\,{{\rm e}^{-t}}+{\frac {3\,{\it \_C4}\,\sin \left ( 3\,t \right ) }{7}}-{\frac {4\,t}{3}} \right \} \right \} \]