\[ \left \{x'(t)+y'(t)=x(t) y(t),y'(t)+z'(t)=y(t) z(t),x'(t)+z'(t)=x(t) z(t)\right \} \] ✗ Mathematica : cpu = 124.617 (sec), leaf count = 0
, could not solve
DSolve[{Derivative[1][x][t] + Derivative[1][y][t] == x[t]*y[t], Derivative[1][y][t] + Derivative[1][z][t] == y[t]*z[t], Derivative[1][x][t] + Derivative[1][z][t] == x[t]*z[t]}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.433 (sec), leaf count = 4259
\[\left [\left \{x \relax (t ) = -\frac {2}{-2 c_{2}+t}\right \}, \{y \relax (t ) = x \relax (t )\}, \left \{z \relax (t ) = \left (\int -\frac {x \relax (t )^{2} {\mathrm e}^{-\left (\int x \relax (t )d t \right )}}{2}d t +c_{1}\right ) {\mathrm e}^{\int x \relax (t )d t}\right \}\right ]\]