\[ \left \{x'(t)=-x(t) (x(t)+y(t)),y'(t)=y(t) (x(t)+y(t))\right \} \] ✓ Mathematica : cpu = 0.0204338 (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 = 0.342 (sec), leaf count = 57
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) = \left ( -t+{\it \_C1} \right ) ^{-1} \right \} ],[ \left \{ x \left ( t \right ) ={\frac {1}{{\it \_C1}}\tanh \left ( {\frac {{\it \_C2}+t}{{\it \_C1}}} \right ) } \right \} , \left \{ y \left ( t \right ) ={\frac {- \left ( x \left ( t \right ) \right ) ^{2}-{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{x \left ( t \right ) }} \right \} ] \right \} \]