\[ \left \{x''(t)-2 x'(t)-y'(t)+y(t)=0,2 x'(t)-x(t)+y^{(3)}(t)-y''(t)=t\right \} \] ✓ Mathematica : cpu = 0.467105 (sec), leaf count = 1132
\[\left \{\left \{x(t)\to \frac {1}{64} e^{-t} \left (2 e^{2 t} t^2-6 e^{2 t} t+7 e^{2 t}+1\right ) \left (e^t (1-t)+e^{-t} \left (-2 t^3-8 t^2-17 t-17\right )\right )+\frac {1}{64} e^{-t} \left (2 e^{2 t} t^2+6 e^{2 t} t+e^{2 t}-1\right ) \left (e^t (t-1)+e^{-t} \left (-2 t^3-4 t^2-7 t-7\right )\right )-\frac {1}{384} e^{-t} \left (2 e^{2 t} t^2+2 e^{2 t} t-e^{2 t}+1\right ) \left (e^t (9 t-9)+e^{-t} \left (-4 t^4-22 t^3-48 t^2-87 t-87\right )\right )+\frac {1}{384} e^{-t} \left (2 e^{2 t} t^2-2 e^{2 t} t+e^{2 t}-1\right ) \left (e^t (9 t-9)+e^{-t} \left (-4 t^4+2 t^3+24 t^2+9 t+9\right )\right )+\frac {1}{192} e^{-t} \left (2 e^{2 t} t-e^{2 t}+1\right ) \left (-e^t (9 t-9)-e^{-t} \left (4 t^4+10 t^3+9 t+9\right )\right )+\frac {1}{8} e^{-t} \left (2 e^{2 t} t^2-6 e^{2 t} t+7 e^{2 t}+1\right ) c_1+\frac {1}{8} e^{-t} \left (2 e^{2 t} t^2+6 e^{2 t} t+e^{2 t}-1\right ) c_2-\frac {1}{8} e^{-t} \left (2 e^{2 t} t^2+2 e^{2 t} t-e^{2 t}+1\right ) c_3+\frac {1}{4} e^{-t} \left (2 e^{2 t} t-e^{2 t}+1\right ) c_4+\frac {1}{8} e^{-t} \left (2 e^{2 t} t^2-2 e^{2 t} t+e^{2 t}-1\right ) c_5,y(t)\to -\frac {1}{384} e^{-t} \left (4 e^{2 t} t^3-18 e^{2 t} t^2+18 e^{2 t} t-9 e^{2 t}+9\right ) \left (e^t (1-t)+e^{-t} \left (-2 t^3-8 t^2-17 t-17\right )\right )-\frac {1}{384} e^{-t} \left (4 e^{2 t} t^3+18 e^{2 t} t^2-18 e^{2 t} t+9 e^{2 t}-9\right ) \left (e^t (t-1)+e^{-t} \left (-2 t^3-4 t^2-7 t-7\right )\right )+\frac {e^{-t} \left (4 e^{2 t} t^3+6 e^{2 t} t^2-30 e^{2 t} t+39 e^{2 t}+9\right ) \left (e^t (9 t-9)+e^{-t} \left (-4 t^4-22 t^3-48 t^2-87 t-87\right )\right )}{2304}-\frac {e^{-t} \left (4 e^{2 t} t^3-6 e^{2 t} t^2-18 e^{2 t} t+9 e^{2 t}-9\right ) \left (e^t (9 t-9)+e^{-t} \left (-4 t^4+2 t^3+24 t^2+9 t+9\right )\right )}{2304}-\frac {1}{384} e^{-t} \left (2 e^{2 t} t^2-2 e^{2 t} t-3 e^{2 t}+3\right ) \left (-e^t (9 t-9)-e^{-t} \left (4 t^4+10 t^3+9 t+9\right )\right )-\frac {1}{48} e^{-t} \left (4 e^{2 t} t^3-18 e^{2 t} t^2+18 e^{2 t} t-9 e^{2 t}+9\right ) c_1-\frac {1}{48} e^{-t} \left (4 e^{2 t} t^3+18 e^{2 t} t^2-18 e^{2 t} t+9 e^{2 t}-9\right ) c_2+\frac {1}{48} e^{-t} \left (4 e^{2 t} t^3+6 e^{2 t} t^2-30 e^{2 t} t+39 e^{2 t}+9\right ) c_3-\frac {1}{8} e^{-t} \left (2 e^{2 t} t^2-2 e^{2 t} t-3 e^{2 t}+3\right ) c_4-\frac {1}{48} e^{-t} \left (4 e^{2 t} t^3-6 e^{2 t} t^2-18 e^{2 t} t+9 e^{2 t}-9\right ) c_5\right \}\right \}\] ✓ Maple : cpu = 0.069 (sec), leaf count = 67
\[\left \{x \relax (t ) = -\frac {2 \,{\mathrm e}^{-t} c_{2}}{3}+\frac {\left (-9 t^{2} c_{5}-6 t c_{4}-3 c_{3}-18 c_{5}\right ) {\mathrm e}^{t}}{3}-t -2, y \relax (t ) = {\mathrm e}^{-t} c_{2}-2+\left (t^{3} c_{5}+t^{2} c_{4}+t c_{3}+c_{1}\right ) {\mathrm e}^{t}\right \}\]