Let $$x = x(y)$$ be the solution of the differential equation
$$2(y+2)\log_e(y+2)dx + (x + 4 - 2\log_e(y+2))dy = 0$$, $$y > -1$$ with $$x(e^4 - 2) = 1$$. Then $$x(e^9 - 2)$$ is equal to

A

$$3$$

B

$$\frac{4}{9}$$

C

$$\frac{32}{9}$$

D

$$\frac{10}{3}$$