Question

Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.

Answer 1

Given y = A sin x ..........(1)

Differentiating with respect to x

`"dy"/"dx" = "A"cos"x"`  ......(2)

From (1) and (2) we have

`"dy"/"dx" = "y"/sin"x" . cos"x"`

⇒ `"dy"/"dx" - (cot"x")"y" = 0`

Thus, this is the required differential equation.