Question

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

Answer 1

Let the general equation of the family of all straight lines passing through the origin is

$y=mx$

On differentiating both sides w.r.t x, we get,

$\frac{dy}{dx}=m$

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

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