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