function rhs = odef3_rhs(eta, Y)

  global C K R

  % careful here if we don't start at 1/R
  if (eta == 1/R)
    rhs = [Y(2);  (Y(2)/R + Y(1))/-4];
  else
    rhs = [Y(2); eta*Y(1) + 2*Y(2)];
  end
