The differential equation of all straight lines passing through origin is

y = \sqrt{x} \frac{d y}{d x}

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\frac{d y}{d x} = y + x

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\frac{d y}{d x} = y - x

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None of these

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Solution

The correct option is C None of these
General equation of straight line passing through origin is y=kx(where k=constant)

$y = k x$

$\frac{d y}{d x} = k$

As, $k = \frac{y}{x}$

$\frac{d y}{d x} = \frac{y}{x}$

$x d y = y d x$

$x d y - y d x = 0 \to$ this is the differential equation of all straight lines passing through origin.

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Similar questions

\frac{d y}{d x} - x = {(\begin{matrix} y - x \frac{d y}{d x} \end{matrix})}^{- 4}

\frac{d y}{d x} + x {(\frac{d y}{d x})}^{2} - y = 0

If $y = c e^{s i n^{- 1} x},$ then corresponding to this the differential equation is

y - x \frac{d y}{d x} = a (y^{2} + \frac{d y}{d x})

y + x \frac{d y}{d x} = x - y \frac{d y}{d x}

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