\[ \left \{x'(t)-y(t)+z(t)=0,-x(t)+y'(t)-y(t)=t,-x(t)+z'(t)-z(t)=t\right \} \] ✓ Mathematica : cpu = 0.0165535 (sec), leaf count = 226
\[\left \{\left \{x(t)\to e^{-t} \left (1-e^t\right ) (-t-1)+e^{-t} \left (e^t-1\right ) (-t-1)+c_2 \left (e^t-1\right )+c_3 \left (1-e^t\right )+c_1,y(t)\to e^{-t} (-t-1) \left (-e^t t+e^t-1\right )+e^{-t} (-t-1) \left (e^t t+1\right )+c_3 \left (-e^t t+e^t-1\right )+c_1 \left (e^t-1\right )+c_2 \left (e^t t+1\right ),z(t)\to e^{-t} (-t-1) \left (-e^t t+2 e^t-1\right )+e^{-t} (-t-1) \left (e^t t-e^t+1\right )+c_3 \left (-e^t t+2 e^t-1\right )+c_1 \left (e^t-1\right )+c_2 \left (e^t t-e^t+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.081 (sec), leaf count = 51
\[\{x \relax (t ) = c_{2}+c_{3} {\mathrm e}^{t}, y \relax (t ) = \left (t c_{3}+c_{1}\right ) {\mathrm e}^{t}-t -c_{2}-1, z \relax (t ) = \left (\left (t -1\right ) c_{3}+c_{1}\right ) {\mathrm e}^{t}-t -c_{2}-1\}\]