\[ \left \{x''(t)+x(t)+y(t)=-5,-4 x(t)+y''(t)-3 y(t)=-3\right \} \] ✓ Mathematica : cpu = 0.11181 (sec), leaf count = 151
\[\left \{\left \{x(t)\to \frac {1}{4} e^{-t} \left (2 c_1 (t+1)-2 c_2 t+c_3 t-c_4 t+e^{2 t} \left (-2 c_1 (t-1)-2 c_2 (t-2)-c_3 t-c_4 t+c_4\right )-4 c_2-c_4+72 e^t\right ),y(t)\to \frac {1}{2} e^{-t} \left (\left (-2 c_1+2 c_2-c_3+c_4\right ) t+e^{2 t} \left (\left (2 c_1+2 c_2+c_3+c_4\right ) t-2 c_2+c_3\right )+2 c_2+c_3-46 e^t\right )\right \}\right \}\]
✓ Maple : cpu = 0.049 (sec), leaf count = 60
\[ \left \{ \left \{ x \left ( t \right ) = \left ( {\it \_C4}\,t+{\it \_C2} \right ) {{\rm e}^{-t}}+18+ \left ( {\it \_C3}\,t+{\it \_C1} \right ) {{\rm e}^{t}},y \left ( t \right ) = \left ( \left ( -2\,t+2 \right ) {\it \_C4}-2\,{\it \_C2} \right ) {{\rm e}^{-t}}-23+ \left ( \left ( -2\,t-2 \right ) {\it \_C3}-2\,{\it \_C1} \right ) {{\rm e}^{t}} \right \} \right \} \]