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