\[ \left \{x'(t)=x(t) (y(t)-z(t)),y'(t)=y(t) (z(t)-x(t)),z'(t)=z(t) (x(t)-y(t))\right \} \] ✗ Mathematica : cpu = 1.5664 (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 = 3.804 (sec), leaf count = 383
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) =0 \right \} , \left \{ z \left ( t \right ) ={\it \_C1} \right \} ],[ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) ={\frac {{\it \_C1}\,{{\rm e}^{{\it \_C2}\,{\it \_C1}}}{{\rm e}^{{\it \_C1}\,t}}}{-1+{{\rm e}^{{\it \_C2}\,{\it \_C1}}}{{\rm e}^{{\it \_C1}\,t}}}} \right \} , \left \{ z \left ( t \right ) ={\frac {{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) }{y \left ( t \right ) }} \right \} ],[ \left \{ x \left ( t \right ) ={\it \_C1} \right \} , \left \{ y \left ( t \right ) =0 \right \} , \left \{ z \left ( t \right ) =0 \right \} ],[ \left \{ x \left ( t \right ) ={\it \_C1} \right \} , \left \{ y \left ( t \right ) =x \left ( t \right ) \right \} , \left \{ z \left ( t \right ) =x \left ( t \right ) \right \} ],[ \left \{ x \left ( t \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_f}}}{\it \_g} \left ( {\it \_f} \right ) ={\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}} \left ( 3\, \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}{{\it \_f}}^{2}+2\, \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}\sqrt {{\frac {3\,{{\it \_f}}^{2}{\it \_g} \left ( {\it \_f} \right ) +{\it \_g} \left ( {\it \_f} \right ) +2\,{\it \_f}}{{\it \_g} \left ( {\it \_f} \right ) }}}+ \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}+5\,{\it \_g} \left ( {\it \_f} \right ) {\it \_f}+1 \right ) } \right \} , \left \{ {\it \_f}={\frac {{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{ \left ( x \left ( t \right ) \right ) ^{2}}},{\it \_g} \left ( {\it \_f} \right ) ={\frac { \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{2}}{ \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) x \left ( t \right ) -2\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}}} \right \} , \left \{ t=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}\,{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}\,{\rm d}{\it \_f}+{\it \_C1},x \left ( t \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {- \left ( {\frac {{\rm d}^{3}}{{\rm d}{t}^{3}}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{2}+ \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( \left ( x \left ( t \right ) \right ) ^{4}+2\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{2}+2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) x \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2} \right ) }{4\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{3}}} \right \} , \left \{ z \left ( t \right ) ={\frac {- \left ( {\frac {{\rm d}^{3}}{{\rm d}{t}^{3}}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{2}+ \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( \left ( x \left ( t \right ) \right ) ^{4}-2\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{2}+2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) x \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2} \right ) }{4\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{3}}} \right \} ] \right \} \]