Let $x=x(y)$ be the solution of the differential equation $2{y}^{2}\frac{dx}{dy}-2xy+{x}^{2}=0,y1,x\left(e\right)=e$. Then $x\left({e}^{2}\right)$ is equal to: [JEE Main 2026, 2 Apr (Shift 2)]

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Let $x=x(y)$ be the solution of the differential equation $2{y}^{2}\frac{dx}{dy}-2xy+{x}^{2}=0,y>1,x\left(e\right)=e$. Then $x\left({e}^{2}\right)$ is equal to: [JEE Main 2026, 2 Apr (Shift 2)]

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

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