\[ \left \{x'(t)=-\left (x(t) \left (x(t)^2+y(t)^2\right )\right )+x(t)+y(t),y'(t)=-y(t) \left (x(t)^2+y(t)^2\right )-x(t)+y(t)\right \} \] ✗ Mathematica : cpu = 0.438796 (sec), leaf count = 0 , could not solve
DSolve[{Derivative[1][x][t] == x[t] + y[t] - x[t]*(x[t]^2 + y[t]^2), Derivative[1][y][t] == -x[t] + y[t] - y[t]*(x[t]^2 + y[t]^2)}, {x[t], y[t]}, t]
✓ Maple : cpu = 4.266 (sec), leaf count = 200
\[\left \{[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}], \left [\left \{x \left (t \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-\frac {-4 \textit {\_a}^{4}-4 \textit {\_a}^{3} \textit {\_}b\left (\textit {\_a} \right )+6 \textit {\_a}^{2} \textit {\_}b\left (\textit {\_a} \right )^{2}+4 \textit {\_a}^{2}-6 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+\sqrt {-\left (4 \textit {\_a}^{4}-4 \textit {\_a}^{2}+4 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )-1\right ) \left (2 \textit {\_a}^{2}-4 \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+1\right )^{2}}+1}{2 \textit {\_a}^{3}}=0\right \}, \left \{\textit {\_a} =x \left (t \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d t}x \left (t \right )\right \}, \left \{t =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , x \left (t \right )=\textit {\_a} \right \}\right ]\right )\right \}, \left \{y \left (t \right ) = \frac {\left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right ) x \left (t \right )^{2}-3 \left (\frac {d}{d t}x \left (t \right )\right )^{2} x \left (t \right )+2 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )^{2}+2 x \left (t \right )^{3}+\frac {d}{d t}x \left (t \right )-x \left (t \right )}{-4 \left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )+2 x \left (t \right )^{2}+1}\right \}\right ]\right \}\]