\[ \left \{x'(t)=x(t) \left (x(t)^2+y(t)^2-1\right )-y(t),y'(t)=y(t) \left (x(t)^2+y(t)^2-1\right )+x(t)\right \} \] ✗ Mathematica : cpu = 0.213963 (sec), leaf count = 0
DSolve[{Derivative[1][x][t] == -y[t] + x[t]*(-1 + x[t]^2 + y[t]^2), Derivative[1][y][t] == x[t] + y[t]*(-1 + x[t]^2 + y[t]^2)},{x[t], y[t]},t]
, could not solve
DSolve[{Derivative[1][x][t] == -y[t] + x[t]*(-1 + x[t]^2 + y[t]^2), Derivative[1][y][t] == x[t] + y[t]*(-1 + x[t]^2 + y[t]^2)}, {x[t], y[t]}, t]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve({diff(x(t),t) = -y(t)+x(t)*(x(t)^2+y(t)^2-1), diff(y(t),t) = x(t)+y(t)*(x(t)^2+y(t)^2-1)})
, result contains DESol or ODESolStruc
\[[\{x \left (t \right ) = 0\}, \{y \left (t \right ) = 0\}]\]