The general solution of the differential equation $\frac{dy}{dx}=-4xy^2$ is given by
Answer & explanation
Correct answer: option 2
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:
$\int y^{-2}dy = \int -4x\,dx$
$\Rightarrow -y^{-1} = -2x^{2} + C$
$\Rightarrow \frac{1}{y} = 2x^{2} + C$
$y = \frac{1}{2x^{2} + C}$