\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =x \left ( t \right ) \left ( y \left ( t \right ) -z \left ( t \right ) \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =y \left ( t \right ) \left ( z \left ( t \right ) -x \left ( t \right ) \right ) ,{\frac {\rm d}{{\rm d}t}}z \left ( t \right ) =z \left ( t \right ) \left ( x \left ( t \right ) -y \left ( t \right ) \right ) \right \} } \]
Mathematica: cpu = 2.251786 (sec), leaf count = 55 \[ \text {DSolve}\left [\left \{x'(t)=x(t) (y(t)-z(t)),y'(t)=y(t) (z(t)-x(t)),z'(t)=z(t) (x(t)-y(t))\right \},\{x(t),y(t),z(t)\},t\right ] \]
Maple: cpu = 0.686 (sec), leaf count = 393 \[ \text {Too large to display} \]