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If the curve y=y(x) is the solution of t...

If the curve `y=y(x)` is the solution of the differential equation `2(x^(2)+x^(5//4))dy-y(x+x^(1//4))dx = 2x^(9//4)dx, x gt 0` which passes through the point `(1, 1-(4)/(3) log_(e )2)`, then the value of y(16) is equal to :

A

`4((31)/(3)-(8)/(3) log_(e ) 3)`

B

`((31)/(3)+(8)/(3)log_(e )3)`

C

`4((31)/(3)+(8)/(3)log_(e )3)`

D

`((31)/(3)-(8)/(3)log_(e )3)`

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