\[ \left \{x'(t)=-x(t) y(t)^2+x(t)+y(t),y'(t)=x(t)^2 y(t)-x(t)-y(t)\right \} \] ✗ Mathematica : cpu = 0.281872 (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 = 2.128 (sec), leaf count = 182
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) =0 \right \} ],[ \left \{ x \left ( t \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +{\frac {1}{2\,{{\it \_a}}^{2}} \left ( -4\,{\it \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{4}+4\,{{\it \_a}}^{5}-2\,{\it \_a}\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+4\,{\it \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{2}-3\,{{\it \_a}}^{3}+\sqrt { \left ( 4\,{{\it \_a}}^{2}-4\,{\it \_b} \left ( {\it \_a} \right ) {\it \_a}+1 \right ) \left ( {{\it \_a}}^{3}+{\it \_a}-{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}+{\it \_b} \left ( {\it \_a} \right ) -{\it \_a} \right ) }=0 \right \} , \left \{ {\it \_a}=x \left ( t \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right \} , \left \{ t=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},x \left ( t \right ) ={\it \_a} \right \} ] \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {1}{ \left ( x \left ( t \right ) \right ) ^{3}+x \left ( t \right ) -{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) } \left ( \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) x \left ( t \right ) +2\, \left ( x \left ( t \right ) -{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( \left ( x \left ( t \right ) \right ) ^{3}-1/2\,x \left ( t \right ) +1/2\,{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \right ) } \right \} ] \right \} \]