If a curve \(y=f(x)\), passing through the point \((1,2)\), is the solution of the differential equation, \(2 x^2 d y=\l…

If a curve \(y=f(x)\), passing through the point \((1,2)\), is the solution of the differential equation, \(2 x^2 d y=\left(2 x y+y^2\right)\) \(d x\), then \(f\left(\frac{1}{2}\right)\) is equal to:

[JEE Main 2020, 2 Sep (Shift 2)]