ODE No. 1920

$$\{x^{\prime }(t)=x(t)(x(t{)}^2+y(t{)}^2-1)-y(t),y^{\prime }(t)=y(t)(x(t{)}^2+y(t{)}^2-1)+x(t)\}$$ ✗ 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

$$[\{x\left(t\right)=0\},\{y\left(t\right)=0\}]$$