dsolve({diff(x(t),t) = -y(t)*(x(t)^2+y(t)^2), diff(y(t),t) = piecewise(2*x(t) <= x(t)^2+y(t)^2,x(t)^2+y(t)^2,(1/2*x(t)-1/2*y(t)^2/x(t))*(x(t)^2+y(t)^2))})