\[ \left \{x''(t)+x(t)+y(t)=-5,-4 x(t)+y''(t)-3 y(t)=-3\right \} \] ✓ Mathematica : cpu = 0.19674 (sec), leaf count = 554
\[\left \{\left \{x(t)\to -\frac {1}{8} e^{-t} \left (e^{-t} (-13 t-10)+e^t (10-13 t)\right ) \left (e^{2 t} t+t-e^{2 t}+1\right )-\frac {1}{8} e^{-t} \left (e^{2 t}-1\right ) t \left (e^{-t} (-13 t-23)+e^t (13 t-23)\right )-\frac {1}{8} e^{-t} \left (e^{2 t} t+t-2 e^{2 t}+2\right ) \left (e^t (13 t-23)+e^{-t} (13 t+23)\right )-\frac {1}{8} e^{-t} \left (e^{2 t} t-t-e^{2 t}-1\right ) \left (e^t (36-13 t)+e^{-t} (13 t+36)\right )-\frac {1}{4} c_4 e^{-t} \left (e^{2 t} t+t-e^{2 t}+1\right )-\frac {1}{2} c_1 e^{-t} \left (e^{2 t} t-t-e^{2 t}-1\right )-\frac {1}{2} c_2 e^{-t} \left (e^{2 t} t+t-2 e^{2 t}+2\right )-\frac {1}{4} c_3 e^{-t} \left (e^{2 t}-1\right ) t,y(t)\to \frac {1}{4} e^{-t} \left (e^{2 t}+1\right ) \left (e^{-t} (-13 t-10)+e^t (10-13 t)\right ) t+\frac {1}{4} e^{-t} \left (e^{2 t}-1\right ) \left (e^t (36-13 t)+e^{-t} (13 t+36)\right ) t+\frac {1}{4} e^{-t} \left (e^{2 t} t-t+e^{2 t}+1\right ) \left (e^{-t} (-13 t-23)+e^t (13 t-23)\right )+\frac {1}{4} e^{-t} \left (e^{2 t} t+t-e^{2 t}+1\right ) \left (e^t (13 t-23)+e^{-t} (13 t+23)\right )+c_1 e^{-t} \left (e^{2 t}-1\right ) t+\frac {1}{2} c_4 e^{-t} \left (e^{2 t}+1\right ) t+c_2 e^{-t} \left (e^{2 t} t+t-e^{2 t}+1\right )+\frac {1}{2} c_3 e^{-t} \left (e^{2 t} t-t+e^{2 t}+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.046 (sec), leaf count = 60
\[ \left \{ \left \{ x \left ( t \right ) = \left ( {\it \_C4}\,t+{\it \_C2} \right ) {{\rm e}^{-t}}+18+ \left ( {\it \_C3}\,t+{\it \_C1} \right ) {{\rm e}^{t}},y \left ( t \right ) = \left ( \left ( -2\,t+2 \right ) {\it \_C4}-2\,{\it \_C2} \right ) {{\rm e}^{-t}}-23+ \left ( \left ( -2\,t-2 \right ) {\it \_C3}-2\,{\it \_C1} \right ) {{\rm e}^{t}} \right \} \right \} \]