\[ \left \{x''(t)+x(t)+y(t)=-5,-4 x(t)+y''(t)-3 y(t)=-3\right \} \] ✓ Mathematica : cpu = 0.103739 (sec), leaf count = 554
\[\left \{\left \{x(t)\to -\frac {1}{4} c_4 e^{-t} \left (e^{2 t} t+t-e^{2 t}+1\right )-\frac {1}{2} c_1 e^{-t} \left (e^{2 t} t-t-e^{2 t}-1\right )-\frac {1}{2} c_2 e^{-t} \left (e^{2 t} t+t-2 e^{2 t}+2\right )-\frac {1}{4} c_3 e^{-t} \left (e^{2 t}-1\right ) t-\frac {1}{8} e^{-t} \left (e^{-t} (-13 t-10)+e^t (10-13 t)\right ) \left (e^{2 t} t+t-e^{2 t}+1\right )-\frac {1}{8} e^{-t} \left (e^{2 t}-1\right ) t \left (e^{-t} (-13 t-23)+e^t (13 t-23)\right )-\frac {1}{8} e^{-t} \left (e^{2 t} t+t-2 e^{2 t}+2\right ) \left (e^t (13 t-23)+e^{-t} (13 t+23)\right )-\frac {1}{8} e^{-t} \left (e^{2 t} t-t-e^{2 t}-1\right ) \left (e^t (36-13 t)+e^{-t} (13 t+36)\right ),y(t)\to c_1 e^{-t} \left (e^{2 t}-1\right ) t+\frac {1}{2} c_4 e^{-t} \left (e^{2 t}+1\right ) t+c_2 e^{-t} \left (e^{2 t} t+t-e^{2 t}+1\right )+\frac {1}{2} c_3 e^{-t} \left (e^{2 t} t-t+e^{2 t}+1\right )+\frac {1}{4} e^{-t} \left (e^{2 t}+1\right ) \left (e^{-t} (-13 t-10)+e^t (10-13 t)\right ) t+\frac {1}{4} e^{-t} \left (e^{2 t}-1\right ) \left (e^t (36-13 t)+e^{-t} (13 t+36)\right ) t+\frac {1}{4} e^{-t} \left (e^{2 t} t-t+e^{2 t}+1\right ) \left (e^{-t} (-13 t-23)+e^t (13 t-23)\right )+\frac {1}{4} e^{-t} \left (e^{2 t} t+t-e^{2 t}+1\right ) \left (e^t (13 t-23)+e^{-t} (13 t+23)\right )\right \}\right \}\]
✓ Maple : cpu = 0.053 (sec), leaf count = 72
\[ \left \{ \left \{ x \left ( t \right ) =18+{\it \_C1}\,{{\rm e}^{t}}+{\it \_C2}\,{{\rm e}^{-t}}+{\it \_C3}\,t{{\rm e}^{t}}+{\it \_C4}\,{{\rm e}^{-t}}t,y \left ( t \right ) =-2\,{\it \_C1}\,{{\rm e}^{t}}-2\,{\it \_C2}\,{{\rm e}^{-t}}-2\,{\it \_C3}\,{{\rm e}^{t}}-2\,{\it \_C3}\,t{{\rm e}^{t}}-2\,{\it \_C4}\,{{\rm e}^{-t}}t+2\,{\it \_C4}\,{{\rm e}^{-t}}-23 \right \} \right \} \]