Observe the following statements:
I. If $dy + 2xy\,dx = 2e^{-x^2}\,dx$, then $ye^{x^2} = 2x + c$
II. If $ye^{-x^2} - 2x = c$, then $dx = (2e^{-x^2} - 2xy)\,dy$
Which of the following is a correct statement?