Question

Find the differential equation of the family of lines passing through the origin.

Answer 1

Equation of lines through origin:

Let equation of lines be: $ax\pm by=0$ and $y=mx$

where, $m⟶slope$

let have equation as $y=mx$

Differentiate

$\Rightarrow \frac{dy}{dx}=m\Rightarrow \frac{dy}{dx}=\frac{y}{x}$