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
$\int y~dy = \int -x~dx$
⇒ $\frac{y^2}{2} = \frac{-x^2}{2} + C$
⇒ $x^2+y^2 = 2C$
⇒ $x^2 + y^2 = C$