Let $y=y(x)$ be the solution curve of the differential equation $\mathrm{x}\left({\mathrm{x}}^{2}+{\mathrm{e}}^{\mathrm{x}}\right)\mathrm{dy}+\left({\mathrm{e}}^{\mathrm{x}}(\mathrm{x}-2)\mathrm{y}-{\mathrm{x}}^{3}\right)\mathrm{dx}=0,$ x 0 passing through the point $(1,0)$. Then $y(2)$ is equal to : [JEE Main 2025, 7 Apr (Shift 1)]

Question

Let $y=y(x)$ be the solution curve of the differential equation $\mathrm{x}\left({\mathrm{x}}^{2}+{\mathrm{e}}^{\mathrm{x}}\right)\mathrm{dy}+\left({\mathrm{e}}^{\mathrm{x}}(\mathrm{x}-2)\mathrm{y}-{\mathrm{x}}^{3}\right)\mathrm{dx}=0,$ x > 0 passing through the point $(1,0)$. Then $y(2)$ is equal to : [JEE Main 2025, 7 Apr (Shift 1)]

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Let \(y=y(x)\) be the solution curve of the differential equation \(\mathrm{x}\left({\mathrm{x}}^{2}+{\mathrm{e}}^{\math…

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