The differential equation $\frac{dy}{dx}+\frac{x}{y}=0$, represents the family of curves:
Answer & explanation
Correct answer: option 4
$\frac{dy}{dx}+\frac{x}{y}=0⇒\frac{dy}{dx}=\frac{-x}{y}$
$y\,dy=-x\,dx$
Integrating both sides
$\int y\,dy=\int-x\,dx$
$⇒\frac{y^2}{2}=\frac{-x^2}{2}+C$
$⇒x^2+y^2=2C$
$⇒x^2+y^2=C$