\[ \left \{x'(t)=-x(t) y(t)^2+x(t)+y(t),y'(t)=x(t)^2 y(t)-x(t)-y(t)\right \} \] ✗ Mathematica : cpu = 0.425184 (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 = 2.908 (sec), leaf count = 184
\[\left \{[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}], \left [\left \{x \left (t \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {4 \textit {\_a}^{5}+2 \textit {\_a}^{2} \textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-3 \textit {\_a}^{3}-2 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )^{2}-\textit {\_a} +\left (-4 \textit {\_a}^{4}+4 \textit {\_a}^{2}+1\right ) \textit {\_}b\left (\textit {\_a} \right )+\sqrt {\left (4 \textit {\_a}^{2}-4 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+1\right ) \left (\textit {\_a}^{3}+\textit {\_a} -\textit {\_}b\left (\textit {\_a} \right )\right )^{2}}}{2 \textit {\_a}^{2}}=0\right \}, \left \{\textit {\_a} =x \left (t \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d t}x \left (t \right )\right \}, \left \{t =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , x \left (t \right )=\textit {\_a} \right \}\right ]\right )\right \}, \left \{y \left (t \right ) = \frac {\left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )+2 \left (-\frac {d}{d t}x \left (t \right )+x \left (t \right )\right ) \left (x \left (t \right )^{3}+\frac {\frac {d}{d t}x \left (t \right )}{2}-\frac {x \left (t \right )}{2}\right )}{x \left (t \right )^{3}-\frac {d}{d t}x \left (t \right )+x \left (t \right )}\right \}\right ]\right \}\]