Let $y=y(x)$ be the solution curve of the differential equation $\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right), x0, y(1)=3$. Then $\frac{y^2(x)}{9}$ is equal to: [JEE Main 2023, 25 Jan (Shift 1)]

Question

Let $y=y(x)$ be the solution curve of the differential equation $\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right), x>0, y(1)=3$. Then $\frac{y^2(x)}{9}$ is equal to: [JEE Main 2023, 25 Jan (Shift 1)]

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Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log…

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