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The differential equation for the family...

The differential equation for the family of curves `y = c\ sinx` can be given by

A

`((dy)/(dx))^(2) = y^(2)cot^(2)x`

B

`((dy)/(dx))^(2)-(sec x(dy)/(dx))^(2)+y^(2) = 0`

C

`((dy)/(dx))^(2)=tan^(2)x`

D

`(dy)/(dx)=y cot x`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`y = c sin x" "(i)`
`therefore" "(dy)/(dx)=c cos x" "(ii)`
From (ii)
`((dy)/(dx))^(2) = c^(2) cos^(2) x" "(iii)`
Putting `c =(y)/(sin x) "from (i)", ((dy)/(dx))^(2) = y^(2) cot^(2) x`
Eliminating c from (i) and (ii), `(dy)/(dx) = y cot x`
Squaring and adding (i) and (ii), `y^(2)+((dy)/(dx))^(2)=c^(2)`
Puttting the value of 'c' form (iii), `y^(2)+((dy)/(dx))^(2)=((dy)/(dx)sec x)^(2)`
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