\[ \left \{x''(t)-2 x'(t)-y'(t)+y(t)=0,2 x'(t)-x(t)+y^{(3)}(t)-y''(t)=t\right \} \] ✓ Mathematica : cpu = 0.196144 (sec), leaf count = 252
\[\left \{\left \{x(t)\to \frac {1}{8} e^{-t} \left (e^{2 t} \left (-2 c_3 t^2+2 c_5 t^2+c_1 \left (2 t^2-6 t+7\right )+c_2 \left (2 t^2+6 t+1\right )-2 c_3 t+4 c_4 t-2 c_5 t+c_3-2 c_4+c_5\right )+c_1-c_2-c_3+2 c_4-c_5-8 e^t (t+2)\right ),y(t)\to \frac {1}{48} e^{-t} \left (e^{2 t} \left (4 c_3 t^3-4 c_5 t^3+6 c_3 t^2-12 c_4 t^2+6 c_5 t^2+c_1 \left (-4 t^3+18 t^2-18 t+9\right )-c_2 \left (4 t^3+18 t^2-18 t+9\right )-30 c_3 t+12 c_4 t+18 c_5 t+39 c_3+18 c_4-9 c_5\right )+9 \left (-c_1+c_2+c_3-2 c_4+c_5\right )-96 e^t\right )\right \}\right \}\]
✓ Maple : cpu = 0.068 (sec), leaf count = 67
\[ \left \{ \left \{ x \left ( t \right ) =-{\frac {2\,{\it \_C2}\,{{\rm e}^{-t}}}{3}}+{\frac { \left ( -9\,{\it \_C5}\,{t}^{2}-6\,{\it \_C4}\,t-3\,{\it \_C3}-18\,{\it \_C5} \right ) {{\rm e}^{t}}}{3}}-t-2,y \left ( t \right ) ={\it \_C2}\,{{\rm e}^{-t}}-2+ \left ( {\it \_C5}\,{t}^{3}+{\it \_C4}\,{t}^{2}+{\it \_C3}\,t+{\it \_C1} \right ) {{\rm e}^{t}} \right \} \right \} \]