Let $y(x)$ be the solution of the differential equation $2{x}^{2}dy+\left({e}^{y}-2x\right)dx=0,x0$. If $y(e)=1$, then $y(1)$ is equal to: [JEE Main 2021, 26 Aug (Shift 2)]

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Let $y(x)$ be the solution of the differential equation $2{x}^{2}dy+\left({e}^{y}-2x\right)dx=0,x>0$. If $y(e)=1$, then $y(1)$ is equal to: [JEE Main 2021, 26 Aug (Shift 2)]

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Let \(y(x)\) be the solution of the differential equation \(2{x}^{2}dy+\left({e}^{y}-2x\right)dx=0,x>0\). If \(y(e)=1\),…

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