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

Answers (1)

$y= A\sin x$
$\Rightarrow y\, cosec x= A$
$\Rightarrow \frac{dy}{dx}\times cosec \, x+y\left ( -cosec\, x\cot x \right )= 0$
$\therefore \frac{dy}{dx}= y\cot x$

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Form the differential equation representing the family of curves by eliminating the arbitrary constant A.

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