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