\[ \left \{x'(t)=\frac {x(t)^2}{2}-\frac {y(t)}{24},y'(t)=2 x(t) y(t)-3 z(t),z'(t)=3 x(t) z(t)-\frac {y(t)^2}{6}\right \} \] ✗ Mathematica : cpu = 61.4015 (sec), leaf count = 0
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] == -1/6*y[t]^2 + 3*x[t]*z[t]},{x[t], y[t], z[t]},t]
, 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] == -1/6*y[t]^2 + 3*x[t]*z[t]}, {x[t], y[t], z[t]}, t]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve({diff(x(t),t) = 1/2*x(t)^2-1/24*y(t), diff(y(t),t) = 2*x(t)*y(t)-3*z(t), diff(z(t),t) = 3*x(t)*z(t)-1/6*y(t)^2})
, result contains DESol or ODESolStruc
\[\left [\{y \left (t \right ) = 0\}, \left \{x \left (t \right ) = \frac {2}{2 c_{1}-t}\right \}, \{z \left (t \right ) = 0\}\right ]\]