\[ \left \{x'(t)-y(t)+z(t)=0,-x(t)+y'(t)-y(t)=t,-x(t)+z'(t)-z(t)=t\right \} \] ✓ Mathematica : cpu = 0.0154918 (sec), leaf count = 109
\[\left \{\left \{x(t)\to \left (c_2-c_3\right ) \left (e^t-1\right )+c_1,y(t)\to c_1 \left (e^t-1\right )+t \left (\left (c_2-c_3\right ) e^t-1\right )+c_3 e^t+c_2-c_3-1,z(t)\to c_1 \left (e^t-1\right )-c_2 e^t+t \left (\left (c_2-c_3\right ) e^t-1\right )+2 c_3 e^t+c_2-c_3-1\right \}\right \}\]
✓ Maple : cpu = 0.065 (sec), leaf count = 51
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{t}},y \left ( t \right ) = \left ( {\it \_C3}\,t+{\it \_C1} \right ) {{\rm e}^{t}}-t-{\it \_C2}-1,z \left ( t \right ) = \left ( \left ( t-1 \right ) {\it \_C3}+{\it \_C1} \right ) {{\rm e}^{t}}-t-{\it \_C2}-1 \right \} \right \} \]