\[ \left \{x'(t)=\frac {x(t)^2}{2}-\frac {y(t)}{24},y'(t)=2 x(t) y(t)-3 z(t),z'(t)=3 x(t) z(t)-\frac {y(t)^2}{6}\right \} \] ✗ Mathematica : cpu = 63.5154 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t]^2/2 - y[t]/24, Derivative[1][y][t] == 2*x[t]*y[t] - 3*z[t], Derivative[1][z][t] == -y[t]^2/6 + 3*x[t]*z[t]}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.915 (sec), leaf count = 377
\[ \left \{ [ \left \{ y \left ( t \right ) =0 \right \} , \left \{ x \left ( t \right ) =-2\, \left ( t-2\,{\it \_C1} \right ) ^{-1} \right \} , \left \{ z \left ( t \right ) =0 \right \} ],[ \left \{ y \left ( t \right ) =256\, \left ( {\it \_C1}\,t+{\it \_C2} \right ) ^{-4} \right \} , \left \{ x \left ( t \right ) ={\frac {1}{6\,y \left ( t \right ) } \left ( -\sqrt {3} \left ( y \left ( t \right ) \right ) ^{{\frac {3}{2}}}+3\,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) },x \left ( t \right ) ={\frac {1}{6\,y \left ( t \right ) } \left ( \sqrt {3} \left ( y \left ( t \right ) \right ) ^{{\frac {3}{2}}}+3\,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) } \right \} , \left \{ z \left ( t \right ) ={\frac {2\,x \left ( t \right ) y \left ( t \right ) }{3}}-{\frac {{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) }{3}} \right \} ],[ \left \{ y \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 {\sqrt {15} \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{3}}{20\,{{\it \_f}}^{2}}\sqrt {-{\frac {{{\it \_f}}^{2} \left ( 3\,{{\it \_f}}^{2}{\it \_g} \left ( {\it \_f} \right ) +12\,{\it \_f}-5\,{\it \_g} \left ( {\it \_f} \right ) \right ) \left ( {\it \_g} \left ( {\it \_f} \right ) {\it \_f}+4 \right ) ^{2}}{ \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{3}}}}}+{\frac { \left ( {\it \_g} \left ( {\it \_f} \right ) \right ) ^{2}}{2}}+{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}}} \right \} , \left \{ {\it \_f}={{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \left ( y \left ( t \right ) \right ) ^{-{\frac {3}{2}}}},{\it \_g} \left ( {\it \_f} \right ) =2\,{\frac { \left ( y \left ( t \right ) \right ) ^{3/2}{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) }{2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) \right ) y \left ( t \right ) -3\, \left ( {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) ^{2}}} \right \} , \left \{ t=\int \!{\frac {{\it \_g} \left ( {\it \_f} \right ) }{{\it \_f}}{\frac {1}{\sqrt {{{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}}}}}}\,{\rm d}{\it \_f}+{\it \_C1},y \left ( t \right ) ={{\rm e}^{\int \!{\it \_g} \left ( {\it \_f} \right ) \,{\rm d}{\it \_f}+{\it \_C2}}} \right \} ] \right ) \right \} , \left \{ x \left ( t \right ) ={\frac {-2\, \left ( {\frac {{\rm d}^{3}}{{\rm d}{t}^{3}}}y \left ( t \right ) \right ) y \left ( t \right ) +3\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) }{-12\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) \right ) y \left ( t \right ) +15\, \left ( {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) ^{2}}} \right \} , \left \{ z \left ( t \right ) ={\frac {-4\, \left ( {\frac {{\rm d}^{3}}{{\rm d}{t}^{3}}}y \left ( t \right ) \right ) \left ( y \left ( t \right ) \right ) ^{2}+18\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) \right ) \left ( {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) y \left ( t \right ) -15\, \left ( {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) ^{3}}{-36\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) \right ) y \left ( t \right ) +45\, \left ( {\frac {\rm d}{{\rm d}t}}y \left ( t \right ) \right ) ^{2}}} \right \} ] \right \} \]