\[ \left \{x'(t)=-x(t) y(t)^2+x(t)+y(t),y'(t)=x(t)^2 y(t)-x(t)-y(t),z'(t)=y(t)^2-x(t)^2\right \} \] ✗ Mathematica : cpu = 0.269557 (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], Derivative[1][z][t] == -x[t]^2 + y[t]^2}, {x[t], y[t], z[t]}, t]
✓ Maple : cpu = 1.998 (sec), leaf count = 305
\[ \left \{ [ \left \{ x \left ( t \right ) =0 \right \} , \left \{ y \left ( t \right ) =0 \right \} , \left \{ z \left ( t \right ) ={\it \_C1} \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\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{\it \_a}-4\,{\it \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{2}+3\,{{\it \_a}}^{3}-{\it \_b} \left ( {\it \_a} \right ) +{\it \_a}-\sqrt {-4\,{{\it \_a}}^{7}{\it \_b} \left ( {\it \_a} \right ) +4\,{{\it \_a}}^{8}+8\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}{{\it \_a}}^{4}-16\,{\it \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{5}+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 \_b} \left ( {\it \_a} \right ) {{\it \_a}}^{3}+6\,{{\it \_a}}^{4}+ \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-2\,{\it \_b} \left ( {\it \_a} \right ) {\it \_a}+{{\it \_a}}^{2}} \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 \_C2},x \left ( t \right ) ={\it \_a} \right \} ] \right ) \right \} , \left \{ y \left ( t \right ) ={\frac {2\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{3}-2\, \left ( x \left ( t \right ) \right ) ^{4}+ \left ( {\frac {\rm d}{{\rm d}t}}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}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) x \left ( t \right ) + \left ( x \left ( t \right ) \right ) ^{2}}{- \left ( x \left ( t \right ) \right ) ^{3}+{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -x \left ( t \right ) }} \right \} , \left \{ z \left ( t \right ) =\int \!{\frac { \left ( x \left ( t \right ) \right ) ^{5}+2\, \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) \left ( x \left ( t \right ) \right ) ^{2}-2\, \left ( x \left ( t \right ) \right ) ^{3}-{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) }{- \left ( x \left ( t \right ) \right ) ^{3}+{\frac {\rm d}{{\rm d}t}}x \left ( t \right ) -x \left ( t \right ) }}\,{\rm d}t+{\it \_C1} \right \} ] \right \} \]