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Let y=g(x) be the solution of the diffe...

Let `y=g(x)` be the solution of the differential equation `sin (dy)/(dx)+y cos x=4x, x in (0,pi)` If y(pi/2)=0`, then `y(pi/6)` is equal to

A

` - 4/9 pi ^2 `

B

` (4)/( 9 sqrt(3) ) pi ^2`

C

` ( -8 ) /( 9 sqrt(3)) pi ^2 `

D

`-(8)/(9) pi ^2`

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The correct Answer is:
D
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