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 [JEE Main 2023, 15 Apr (Shift 1)]

Question

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 [JEE Main 2023, 15 Apr (Shift 1)]

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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…

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