\[ \left \{x'(t)=y(t)-z(t),y'(t)=x(t)+y(t),z'(t)=x(t)+z(t)\right \} \] ✓ Mathematica : cpu = 0.0113479 (sec), leaf count = 105
\[\left \{\left \{x(t)\to c_2 \left (e^t-1\right )+c_3 \left (1-e^t\right )+c_1,y(t)\to c_1 \left (e^t-1\right )+c_2 \left (e^t t+1\right )+c_3 \left (-e^t t+e^t-1\right ),z(t)\to c_1 \left (e^t-1\right )+c_2 \left (e^t t-e^t+1\right )+c_3 \left (-e^t t+2 e^t-1\right )\right \}\right \}\]
✓ Maple : cpu = 0.06 (sec), leaf count = 48
\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{t}},y \left ( t \right ) ={\it \_C3}\,t{{\rm e}^{t}}+{\it \_C1}\,{{\rm e}^{t}}-{\it \_C2},z \left ( t \right ) ={\it \_C3}\,t{{\rm e}^{t}}+{\it \_C1}\,{{\rm e}^{t}}-{\it \_C3}\,{{\rm e}^{t}}-{\it \_C2} \right \} \right \} \]