\[ \left \{x'(t)=-x(t) y(t)^2+x(t)+y(t),y'(t)=x(t)^2 y(t)-x(t)-y(t)\right \} \] ✗ Mathematica : cpu = 0.116453 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t] + y[t] - x[t]*y[t]^2, Derivative[1][y][t] == -x[t] - y[t] + x[t]^2*y[t]}, {x[t], y[t]}, t]
✓ Maple : cpu = 2.084 (sec), leaf count = 245
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) =0 \right \} ],[ \left \{ x \left ( t \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -{\frac {1}{2\,{{\it \_a}}^{2}} \left ( 4\,{\it \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{4}-4\,{{\it \_a}}^{5}+2\,{\it \_a}\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-4\,{{\it \_a}}^{2}{\it \_b} \left ( {\it \_a} \right ) +3\,{{\it \_a}}^{3}-{\it \_b} \left ( {\it \_a} \right ) -\sqrt {-4\,{\it \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{7}+4\,{{\it \_a}}^{8}+8\,{{\it \_a}}^{4} \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-16\,{{\it \_a}}^{5}{\it \_b} \left ( {\it \_a} \right ) +9\,{{\it \_a}}^{6}-4\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}{\it \_a}+12\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{{\it \_a}}^{2}-14\,{{\it \_a}}^{3}{\it \_b} \left ( {\it \_a} \right ) +6\,{{\it \_a}}^{4}+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-2\,{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +{{\it \_a}}^{2}}+{\it \_a} \right ) }=0 \right \} , \left \{ {\it \_a}=x \left ( t \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right \} , \left \{ t=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},x \left ( t \right ) ={\it \_a} \right \} ] \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {-2\, \left ( x \left ( t \right ) \right ) ^{4}+2\, \left ( x \left ( t \right ) \right ) ^{3}{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) - \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) x \left ( t \right ) + \left ( x \left ( t \right ) \right ) ^{2}-2\,x \left ( t \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) + \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) ^{2}}{- \left ( x \left ( t \right ) \right ) ^{3}-x \left ( t \right ) +{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }} \right \} ] \right \} \]