#### 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

Is there an error in this question or solution?

Solution Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants. Concept: Formation of a Differential Equation Whose General Solution is Given.