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Question
Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.
Solution
The equation of the family of curves is v=A/r+B, where A and B are arbitrary constants.
We have
v=Ar+B
Differentiating both sides with respect to r, we get
`(dv)/(dr)=-A/r^2+0`
`⇒r^2(dv)/(dr)=−A`
Again, differentiating both sides with respect to r, we get
`r^2xx(d^2v)/(d^2r)+2rxx(dv)/(dr)=0`
`⇒r(d^2v)/(d^2r)+2(dv)/(dr)=0`
This is the differential equation representing the family of the given curves
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