I'm trying to solve and plot the following in Mathematica:

eqns = {x'[t] == 
    x[t] - y[t] - 
     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 
   y'[t] == 
    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 
     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};
DSolve[eqns, {x, y}, t]

This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.