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

Solve `sinx(dy)/(dx)=ylny` 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)`

Verified by Experts

The correct Answer is:

A

`because (dy)/(ylny)=(dx)/(sinx)implies ln|lny|=tanx//2|+lnc`
Put `x=(pi)/(2) implies y=2" "therefore y=e^(tan(x//2))`.

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