1.

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

Answer» The equation of the given family of curves is `y=mx" "…(i),` where m is constant. Since the given equation contains one arbitrary constant, we differentiate it once only. On differentiating (i) w.r.t.x, we get
`(dy)/(dx)=m" "…(ii)`
Putting this value of m from (ii) in (i), we get
`y=((dy)/(dx))ximplies((dy)/(dx))-y=0.`
Hence, `x((dy)/(dx))-y=0` is the required differential equation.


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