\[ \left \{x'(t)=-x(t) (x(t)+y(t)),y'(t)=y(t) (x(t)+y(t))\right \} \] ✓ Mathematica : cpu = 0.0520064 (sec), leaf count = 52
\[\left \{\left \{y(t)\to -\sqrt {c_1} \cot \left (\sqrt {c_1} \left (t-c_2\right )\right ),x(t)\to -\sqrt {c_1} \tan \left (\sqrt {c_1} \left (t-c_2\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.146 (sec), leaf count = 57
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) = \left ( {\it \_C1}-t \right ) ^{-1} \right \} ],[ \left \{ x \left ( t \right ) ={\frac {1}{{\it \_C1}}\tanh \left ( {\frac {{\it \_C2}+t}{{\it \_C1}}} \right ) } \right \} , \left \{ y \left ( t \right ) ={\frac {- \left ( x \left ( t \right ) \right ) ^{2}-{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{x \left ( t \right ) }} \right \} ] \right \} \]