For the exact differential equation,

$$\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$$

which one of the following is the solution?

- $u^{2} + 2x^{2} =$ constant
- $xu^{2} + u =$ constant
- $\frac{1}{2}x^{2}u^{2} + 2u =$ constant
- $\frac{1}{2}ux^{2} + 2x =$ constant