\[ \left \{x'(t)=-x(t) (x(t)+y(t)),y'(t)=y(t) (x(t)+y(t))\right \} \] ✓ Mathematica : cpu = 0.0339279 (sec), leaf count = 64
\[\left \{\left \{y(t)\to -\sqrt {c_1} \cot \left (\sqrt {c_1} t-\sqrt {c_1} c_2\right ),x(t)\to -\sqrt {c_1} \tan \left (\sqrt {c_1} t-\sqrt {c_1} c_2\right )\right \}\right \}\] ✓ Maple : cpu = 0.185 (sec), leaf count = 57
\[\left \{\left [\{x \left (t \right ) = 0\}, \left \{y \left (t \right ) = \frac {1}{c_{1}-t}\right \}\right ], \left [\left \{x \left (t \right ) = \frac {\tanh \left (\frac {c_{2}+t}{c_{1}}\right )}{c_{1}}\right \}, \left \{y \left (t \right ) = \frac {-x \left (t \right )^{2}-\frac {d}{d t}x \left (t \right )}{x \left (t \right )}\right \}\right ]\right \}\]