Sum

Form the differential equation representing the family of curves *y* = *mx*, where *m* is an arbitrary constant.

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#### Solution

We have,

*y* = *mx* .........(1)

Differentiating both sides, we get

\[\frac{dy}{dx} = m\]

\[ \Rightarrow \frac{dy}{dx} = \frac{y}{x} ............\left[\text{From (1)} \right]\]

\[ \Rightarrow x\frac{dy}{dx} = y\]

\[ \Rightarrow x\frac{dy}{dx} - y = 0\]

Is there an error in this question or solution?

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