Write the differential equation representing the family of curves `y=m x ,` where m is an arbitrary constant.

Explanation

The given family of curves represents the equation of straight lines.

`∴ y = mx ………. (1)`

Differentiate w.r.t x, we get dy

`dy/dx = m`

∴ substitute m = dy/dx, we have

` y = mx`

`⇒ y = dy/dx x`

`dy/dx = y/x`

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