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Solve sinx*(dy)/(dx)=y*lny if y=e, when ...

Solve `sinx*(dy)/(dx)=y*lny` if y=e, when `x=pi/2`

A

`y=e^(tan(x//2))`

B

`y=e^(-tan^((x//4)))`

C

`y=e^(cotx)`

D

`y=e^(tanx)`

Text Solution

Verified by Experts

The correct Answer is:
A
`because" "(dy)/(ylny)=(dx)/(sinx)rArr ln|lny|=ln|tanx//2|+lnc`
`"Put "x=(pi)/(2)" "rArr" "y=e" "therefore" "y=e^(tan(x//2))`
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