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Q.

The differential equation of all straight lines passing through the origin is:

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a

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

b

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

c

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

d

None of these

answer is C.

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Detailed Solution

The equation of all straight lines passing through the origin is

y = mx ... (i)

where m is arbitrary constant Differentiate (i) w.r.t. x, we get

$\frac{d y}{d x} = m \Rightarrow \frac{d y}{d x} = \frac{y}{x}$ By(i)

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