Let \(x=x(y)\) be the solution of the differential equation \({\mathrm{y}}^{2}\mathrm{dx}+\left(\mathrm{x}-\frac{1}{\mat…

Let \(x=x(y)\) be the solution of the differential equation \({\mathrm{y}}^{2}\mathrm{dx}+\left(\mathrm{x}-\frac{1}{\mathrm{y}}\right)\mathrm{dy}=0\). If \(x(1)=1,\) then \(x\left(\frac{1}{2}\right)\) is:

[JEE Main 2025, 22 Jan (Shift 1)]