\[ \left \{x'(t)=x(t) \left (y(t)^2-z(t)^2\right ),y'(t)=y(t) \left (z(t)^2-x(t)^2\right ),z'(t)=z(t) \left (x(t)^2-y(t)^2\right )\right \} \] ✗ Mathematica : cpu = 0.0432276 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t]*(y[t]^2 - z[t]^2), Derivative[1][y][t] == y[t]*(-x[t]^2 + z[t]^2), Derivative[1][z][t] == (x[t]^2 - y[t]^2)*z[t]}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 2.276 (sec), leaf count = 741
\[\left \{[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}, \{z \left (t \right ) = c_{1}\}], \left [\{x \left (t \right ) = 0\}, \left \{y \left (t \right ) = \frac {\sqrt {c_{1} \left ({\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-1\right ) {\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}}}{{\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-1}, y \left (t \right ) = -\frac {\sqrt {c_{1} \left ({\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-1\right ) {\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}}}{{\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-1}\right \}, \left \{z \left (t \right ) = \frac {\sqrt {\left (\frac {d}{d t}y \left (t \right )\right ) y \left (t \right )}}{y \left (t \right )}, z \left (t \right ) = -\frac {\sqrt {\left (\frac {d}{d t}y \left (t \right )\right ) y \left (t \right )}}{y \left (t \right )}\right \}\right ], [\{x \left (t \right ) = c_{1}\}, \{y \left (t \right ) = -x \left (t \right )\}, \{z \left (t \right ) = -x \left (t \right )\}], [\{x \left (t \right ) = c_{1}\}, \{y \left (t \right ) = -x \left (t \right )\}, \{z \left (t \right ) = x \left (t \right )\}], [\{x \left (t \right ) = c_{1}\}, \{y \left (t \right ) = x \left (t \right )\}, \{z \left (t \right ) = -x \left (t \right )\}], [\{x \left (t \right ) = c_{1}\}, \{y \left (t \right ) = x \left (t \right )\}, \{z \left (t \right ) = x \left (t \right )\}], \left [\left \{x \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 {4 \left (3 \textit {\_f}^{2}+2 \sqrt {\frac {3 \textit {\_f}^{2} \textit {\_g} \left (\textit {\_f} \right )+\textit {\_f} +\textit {\_g} \left (\textit {\_f} \right )}{\textit {\_g} \left (\textit {\_f} \right )}}+1\right ) \textit {\_g} \left (\textit {\_f} \right )^{3}}{\textit {\_f}}+10 \textit {\_g} \left (\textit {\_f} \right )^{2}+\frac {\textit {\_g} \left (\textit {\_f} \right )}{\textit {\_f}}\right \}, \left \{\textit {\_f} =\frac {\frac {d}{d t}x \left (t \right )}{x \left (t \right )^{3}}, \textit {\_g} \left (\textit {\_f} \right )=\frac {\left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{3}}{\left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )-3 \left (\frac {d}{d t}x \left (t \right )\right )^{2}}\right \}, \left \{t =c_{1}+\int \frac {\textit {\_g} \left (\textit {\_f} \right ) {\mathrm e}^{-2 c_{2}+\int -2 \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}}{\textit {\_f}}d \textit {\_f} , x \left (t \right )={\mathrm e}^{c_{2}+\int \textit {\_g} \left (\textit {\_f} \right )d \textit {\_f}}\right \}\right ]\right )\right \}, \left \{y \left (t \right ) = -\frac {\sqrt {-\left (\frac {d^{3}}{d t^{3}}x \left (t \right )\right ) \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+4 \left (\left (x \left (t \right )^{3}+2 \frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+\frac {\frac {d^{2}}{d t^{2}}x \left (t \right )}{4}\right ) \left (\frac {d}{d t}x \left (t \right )\right )^{2} x \left (t \right )}}{4 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}}, y \left (t \right ) = \frac {\sqrt {-\left (\frac {d^{3}}{d t^{3}}x \left (t \right )\right ) \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+4 \left (\left (x \left (t \right )^{3}+2 \frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+\frac {\frac {d^{2}}{d t^{2}}x \left (t \right )}{4}\right ) \left (\frac {d}{d t}x \left (t \right )\right )^{2} x \left (t \right )}}{4 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}}\right \}, \left \{z \left (t \right ) = \frac {\sqrt {\left (x \left (t \right ) y \left (t \right )^{2}-\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )}}{x \left (t \right )}, z \left (t \right ) = -\frac {\sqrt {\left (x \left (t \right ) y \left (t \right )^{2}-\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )}}{x \left (t \right )}\right \}\right ], \left [\left \{x \left (t \right ) = \frac {\sqrt {c_{1} {\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-c_{1} {\mathrm e}^{4 c_{1} c_{2}} {\mathrm e}^{4 c_{1} t}}}{{\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-1}, x \left (t \right ) = -\frac {\sqrt {c_{1} {\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-c_{1} {\mathrm e}^{4 c_{1} c_{2}} {\mathrm e}^{4 c_{1} t}}}{{\mathrm e}^{2 c_{1} c_{2}} {\mathrm e}^{2 c_{1} t}-1}\right \}, \{y \left (t \right ) = 0\}, \left \{z \left (t \right ) = \frac {\sqrt {-\left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )}}{x \left (t \right )}, z \left (t \right ) = -\frac {\sqrt {-\left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )}}{x \left (t \right )}\right \}\right ]\right \}\]