JEE Math Practice Question
Let $x=x(y)$ be the solution of the differential equation $2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y>-1$ with $x\left(e^{4}-2\right)=1$. Then $x\left(e^{9}-2\right)$ is equal to :
- A.$\frac{4}{9}$
- B.$\frac{32}{9}$
- C.$\frac{10}{3}$
- D.3
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