| Find the differential equation of the family of curves represented by where k is an arbitrary constant.

A.

B.

C.

D.

### Right Answer is: C

#### SOLUTION

The given equation ………..(1)

Differentiating w.r.t. x, we get

⇒ ……………..(2)

Dividing (2) by (1), we get

⇒

⇒

⇒

⇒

Substituting this value of k in (2), we get

⇒

⇒ .

⇒

⇒