\[ \left \{x'(t)=y(t)-z(t),y'(t)=x(t)^2+y(t),z'(t)=x(t)^2+z(t)\right \} \] ✓ Mathematica : cpu = 0.0337943 (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 = 0.092 (sec), leaf count = 45
\[\{[\{x \left (t \right ) = c_{2} {\mathrm e}^{t}+c_{3}\}, \{y \left (t \right ) = \left (c_{1}+\int {\mathrm e}^{-t} x \left (t \right )^{2}d t \right ) {\mathrm e}^{t}\}, \{z \left (t \right ) = -\frac {d}{d t}x \left (t \right )+y \left (t \right )\}]\}\]