Question

The differential -equation of the family of lines passing through the origin is

• A. $x = y \frac{dy}{dx} $
• B. $x + y \frac{dy}{dx} = 0 $
• C. $ \frac{dy}{dx} = 0 $
• D. $y = x \frac{dy}{dx} $

Answer 1

Answer: (D)

Equation of line passing. through-the origin is $y = cx $ .........(i)
Differentiating (i) w.r.t, x, we get
$\frac{dy}{dx} = c \:\: \Rightarrow \frac{dy}{dx} = \frac{y}{x}$ (From(i))
$ \Rightarrow \: y = x \frac{dy}{dx}$