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The differential equation of the family of lines through the origin is : |
$x\frac{dy}{dx}- y = 0 $ $x\frac{dy}{dx}+ y = 0 $ $y-x\frac{dx}{dy}=0$ $y+x\frac{dx}{dy}=0$ |
$x\frac{dy}{dx}- y = 0 $ |
The correct answer is Option (1) → $x\frac{dy}{dx}- y = 0$ family of lines passing through O, $⇒y=mx$ differentiating w.r.t.(x) $\frac{dy}{dx}=m$ so $\frac{dy}{dx}=\frac{y}{x}⇒x\frac{dy}{dx}- y = 0 $ |
