The solution of the differential equation $2x\frac{dy}{dx}-y=3$ represents a family of :

Parabolas

The correct answer is Option (1) → Parabolas

$2x\frac{dy}{dx}-y=3$ so $\frac{dy}{dx}=\frac{y+3}{2x}$

so $\int\frac{1}{y+3}dy=\int\frac{1}{2x}dx$

so $\log(y+3)=2\log(2x)+\log(C)$

so $\log(y+3)=\log(Cx^2)$

so $y+3=Cx^2$ → represents family of paprabola