\[ \left \{x'(t)=x(t) (y(t)-z(t)),y'(t)=y(t) (z(t)-x(t)),z'(t)=z(t) (x(t)-y(t))\right \} \] ✗ Mathematica : cpu = 2.74736 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t]*(y[t] - z[t]), Derivative[1][y][t] == y[t]*(-x[t] + z[t]), Derivative[1][z][t] == (x[t] - y[t])*z[t]}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.242 (sec), leaf count = 383
\[\left \{[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}, \{z \left (t \right ) = c_{1}\}], \left [\{x \left (t \right ) = 0\}, \left \{y \left (t \right ) = \frac {c_{1} {\mathrm e}^{c_{1} c_{2}} {\mathrm e}^{c_{1} t}}{{\mathrm e}^{c_{1} c_{2}} {\mathrm e}^{c_{1} t}-1}\right \}, \left \{z \left (t \right ) = \frac {\frac {d}{d t}y \left (t \right )}{y \left (t \right )}\right \}\right ], [\{x \left (t \right ) = c_{1}\}, \{y \left (t \right ) = 0\}, \{z \left (t \right ) = 0\}], [\{x \left (t \right ) = c_{1}\}, \{y \left (t \right ) = x \left (t \right )\}, \{z \left (t \right ) = x \left (t \right )\}], \left [\left \{x \left (t \right ) = \mathit {ODESolStruc} \left ({\mathrm e}^{c_{2}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}, \left [\left \{\frac {d}{d \textit {\_f}}\textit {\_g} \left (\textit {\_f} \right )=\frac {\left (3 \textit {\_f}^{2} \textit {\_g} \left (\textit {\_f} \right )^{2}+5 \textit {\_f} \textit {\_g} \left (\textit {\_f} \right )+2 \sqrt {\frac {3 \textit {\_f}^{2} \textit {\_g} \left (\textit {\_f} \right )+2 \textit {\_f} +\textit {\_g} \left (\textit {\_f} \right )}{\textit {\_g} \left (\textit {\_f} \right )}}\, \textit {\_g} \left (\textit {\_f} \right )^{2}+\textit {\_g} \left (\textit {\_f} \right )^{2}+1\right ) \textit {\_g} \left (\textit {\_f} \right )}{\textit {\_f}}\right \}, \left \{\textit {\_f} =\frac {\frac {d}{d t}x \left (t \right )}{x \left (t \right )^{2}}, \textit {\_g} \left (\textit {\_f} \right )=\frac {\left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}}{\left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )-2 \left (\frac {d}{d t}x \left (t \right )\right )^{2}}\right \}, \left \{t =c_{1}+\int \frac {\textit {\_g} \left (\textit {\_f} \right ) {\mathrm e}^{-c_{2}+\int -\textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}}{\textit {\_f}}d \textit {\_f} , x \left (t \right )={\mathrm e}^{c_{2}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}\right \}\right ]\right )\right \}, \left \{y \left (t \right ) = \frac {-\left (\frac {d^{3}}{d t^{3}}x \left (t \right )\right ) x \left (t \right )^{2}+\left (x \left (t \right )^{4}+2 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+2 \left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )-\left (\frac {d}{d t}x \left (t \right )\right )^{2}\right ) \left (\frac {d}{d t}x \left (t \right )\right )}{4 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{3}}\right \}, \left \{z \left (t \right ) = \frac {-\left (\frac {d^{3}}{d t^{3}}x \left (t \right )\right ) x \left (t \right )^{2}+\left (x \left (t \right )^{4}-2 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+2 \left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )-\left (\frac {d}{d t}x \left (t \right )\right )^{2}\right ) \left (\frac {d}{d t}x \left (t \right )\right )}{4 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{3}}\right \}\right ]\right \}\]