\[ \left \{x'(t)=y(t)-z(t),y'(t)=x(t)^2+y(t),z'(t)=x(t)^2+z(t)\right \} \] ✓ Mathematica : cpu = 0.0329601 (sec), leaf count = 308
DSolve[{Derivative[1][x][t] == y[t] - z[t], Derivative[1][y][t] == x[t]^2 + y[t], Derivative[1][z][t] == x[t]^2 + z[t]},{x[t], y[t], z[t]},t]
\[\left \{\left \{x(t)\to e^{-c_3} \left (e^t+e^{c_3} c_1\right ),y(t)\to c_2 \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )+\left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right ) \left (-\frac {c_1{}^2}{e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1}+e^{-c_3} \left (e^t+e^{c_3} c_1\right )+2 c_1 \log \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )\right ),z(t)\to -e^{-c_3} \left (e^t+e^{c_3} c_1\right )+c_2 \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )+\left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right ) \left (-\frac {c_1{}^2}{e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1}+e^{-c_3} \left (e^t+e^{c_3} c_1\right )+2 c_1 \log \left (e^{-c_3} \left (e^t+e^{c_3} c_1\right )-c_1\right )\right )+c_1\right \}\right \}\] ✓ Maple : cpu = 0.064 (sec), leaf count = 45
dsolve({diff(x(t),t) = y(t)-z(t), diff(y(t),t) = x(t)^2+y(t), diff(z(t),t) = x(t)^2+z(t)})
\[[\{x \left (t \right ) = c_{2}+c_{3} {\mathrm e}^{t}\}, \{y \left (t \right ) = \left (\int x \left (t \right )^{2} {\mathrm e}^{-t}d t +c_{1}\right ) {\mathrm e}^{t}\}, \{z \left (t \right ) = -\frac {d}{d t}x \left (t \right )+y \left (t \right )\}]\]