\[ \left \{x'(t)=y(t)-z(t),y'(t)=x(t)^2+y(t),z'(t)=x(t)^2+z(t)\right \} \] ✓ Mathematica : cpu = 0.030861 (sec), leaf count = 308
\[\left \{\left \{x(t)\to e^{-c_3} \left (e^t+e^{c_3} c_1\right ),y(t)\to c_2 \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )+\left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right ) \left (-\frac {c_1{}^2}{e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1}+e^{-c_3} \left (e^t+e^{c_3} c_1\right )+2 c_1 \log \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )\right ),z(t)\to -e^{-c_3} \left (e^t+e^{c_3} c_1\right )+c_2 \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )+\left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right ) \left (-\frac {c_1{}^2}{e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1}+e^{-c_3} \left (e^t+e^{c_3} c_1\right )+2 c_1 \log \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )\right )+c_1\right \}\right \}\] ✓ Maple : cpu = 0.084 (sec), leaf count = 45
\[ \left \{ [ \left \{ x \left ( t \right ) ={\it \_C2}+{\it \_C3}\,{{\rm e}^{t}} \right \} , \left \{ y \left ( t \right ) = \left ( \int \! \left ( x \left ( t \right ) \right ) ^{2}{{\rm e}^{-t}}\,{\rm d}t+{\it \_C1} \right ) {{\rm e}^{t}} \right \} , \left \{ z \left ( t \right ) =-{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) +y \left ( t \right ) \right \} ] \right \} \]