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

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Sum

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

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Solution

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.
Concept: Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
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