The solution of the differential equation $2x\frac{dy}{dx}-y=3$ represents a family of :
Answer & explanation
Correct answer: option 1
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