\[ \left \{x'(t)-y(t)+z(t)=0,-x(t)+y'(t)-y(t)=t,-x(t)+z'(t)-z(t)=t\right \} \] ✓ Mathematica : cpu = 0.0161429 (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 = 0.188 (sec), leaf count = 51
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{t}},y \left ( t \right ) = \left ( {\it \_C3}\,t+{\it \_C1} \right ) {{\rm e}^{t}}-t-{\it \_C2}-1,z \left ( t \right ) = \left ( \left ( t-1 \right ) {\it \_C3}+{\it \_C1} \right ) {{\rm e}^{t}}-t-{\it \_C2}-1 \right \} \right \} \]