The differential equation of the family of lines through the origin, is
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : $x\frac{dy}{dx}-y=0$
The equation of the family of lines passing through the origin is
$y = mx $ ............(i)
$⇒\frac{dy}{dx}= m$
From (i) and (ii), we get
$y=x\frac{dy}{dx}, $ which is the required differential equation.