\[ \left \{x'(t)=-\left (x(t) \left (x(t)^2+y(t)^2\right )\right )+x(t)+y(t),y'(t)=-y(t) \left (x(t)^2+y(t)^2\right )-x(t)+y(t)\right \} \] ✗ Mathematica : cpu = 0.401214 (sec), leaf count = 0
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]
, 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 = 0. (sec), leaf count = 0
dsolve({diff(x(t),t) = x(t)+y(t)-x(t)*(x(t)^2+y(t)^2), diff(y(t),t) = -x(t)+y(t)-y(t)*(x(t)^2+y(t)^2)})
, result contains DESol or ODESolStruc
\[[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}]\]