The general solution of the differential equation $\frac{dy}{dx}=-4xy^2$ is given by

$2x^2-\frac{1}{y}= C$: C is an arbitrary constant

The correct answer is Option (2) → $2x^2-\frac{1}{y}= C$: C is an arbitrary constant

$\frac{dy}{dx} = -4xy^{2}$

Separate variables:

$\frac{dy}{y^{2}} = -4x\,dx$

Integrate both sides:

$\int y^{-2}dy = \int -4x\,dx$

$\Rightarrow -y^{-1} = -2x^{2} + C$

$\Rightarrow \frac{1}{y} = 2x^{2} + C$

$y = \frac{1}{2x^{2} + C}$