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

Question

Let $y(x)$ be the solution of the differential equation $2 x^2 d y$ $+\left(e^y-2 x\right) d x=0, x>0$. 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 \(2 x^2 d y\) \(+\left(e^y-2 x\right) d x=0, x>0\). If \(y(…

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Let \(y(x)\) be the solution of the differential equation \(2 x^2 d y\) \(+\left(e^y-2 x\right) d x=0, x&gt;0\). If \(y(…

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