\[ \left \{x'(t)=\frac {x(t)^2}{2}-\frac {y(t)}{24},y'(t)=2 x(t) y(t)-3 z(t),z'(t)=3 x(t) z(t)-\frac {y(t)^2}{6}\right \} \] ✗ Mathematica : cpu = 67.4084 (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] == -1/6*y[t]^2 + 3*x[t]*z[t]}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.512 (sec), leaf count = 377
\[\left \{\left [\{y \left (t \right ) = 0\}, \left \{x \left (t \right ) = -\frac {2}{-2 c_{1}+t}\right \}, \{z \left (t \right ) = 0\}\right ], \left [\left \{y \left (t \right ) = \frac {256}{\left (c_{1} t +c_{2}\right )^{4}}\right \}, \left \{x \left (t \right ) = \frac {-\sqrt {3}\, y \left (t \right )^{\frac {3}{2}}+3 \frac {d}{d t}y \left (t \right )}{6 y \left (t \right )}, x \left (t \right ) = \frac {\sqrt {3}\, y \left (t \right )^{\frac {3}{2}}+3 \frac {d}{d t}y \left (t \right )}{6 y \left (t \right )}\right \}, \left \{z \left (t \right ) = \frac {2 x \left (t \right ) y \left (t \right )}{3}-\frac {\frac {d}{d t}y \left (t \right )}{3}\right \}\right ], \left [\left \{y \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 {\textit {\_g} \left (\textit {\_f} \right )^{2}}{2}+\frac {\sqrt {-\frac {\left (3 \textit {\_f}^{2} \textit {\_g} \left (\textit {\_f} \right )+12 \textit {\_f} -5 \textit {\_g} \left (\textit {\_f} \right )\right ) \left (\textit {\_f} \textit {\_g} \left (\textit {\_f} \right )+4\right )^{2} \textit {\_f}^{2}}{\textit {\_g} \left (\textit {\_f} \right )^{3}}}\, \sqrt {15}\, \textit {\_g} \left (\textit {\_f} \right )^{3}}{20 \textit {\_f}^{2}}+\frac {\textit {\_g} \left (\textit {\_f} \right )}{\textit {\_f}}\right \}, \left \{\textit {\_f} =\frac {\frac {d}{d t}y \left (t \right )}{y \left (t \right )^{\frac {3}{2}}}, \textit {\_g} \left (\textit {\_f} \right )=\frac {2 \left (\frac {d}{d t}y \left (t \right )\right ) y \left (t \right )^{\frac {3}{2}}}{2 \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right ) y \left (t \right )-3 \left (\frac {d}{d t}y \left (t \right )\right )^{2}}\right \}, \left \{t =c_{1}+\int \frac {\textit {\_g} \left (\textit {\_f} \right )}{\textit {\_f} \sqrt {{\mathrm e}^{c_{2}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}}}d \textit {\_f} , y \left (t \right )={\mathrm e}^{c_{2}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}\right \}\right ]\right )\right \}, \left \{x \left (t \right ) = \frac {-2 \left (\frac {d^{3}}{d t^{3}}y \left (t \right )\right ) y \left (t \right )+3 \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right ) \left (\frac {d}{d t}y \left (t \right )\right )}{-12 \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right ) y \left (t \right )+15 \left (\frac {d}{d t}y \left (t \right )\right )^{2}}\right \}, \left \{z \left (t \right ) = \frac {-4 \left (\frac {d^{3}}{d t^{3}}y \left (t \right )\right ) y \left (t \right )^{2}+18 \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right ) \left (\frac {d}{d t}y \left (t \right )\right ) y \left (t \right )-15 \left (\frac {d}{d t}y \left (t \right )\right )^{3}}{-36 \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right ) y \left (t \right )+45 \left (\frac {d}{d t}y \left (t \right )\right )^{2}}\right \}\right ]\right \}\]