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If y=y(x) satisfies the differential equ...

If `y=y(x)` satisfies the differential equation
`8sqrt(x)(sqrt(9+sqrt(x)))dy=(sqrt(4+sqrt(9+sqrt(x))))^(-1)` dx
`x gt 0` and `y(0)=sqrt(7)`, then `y(256)`=

A

(a) 16

B

(b) 3

C

(c) 9

D

(d) 80

Text Solution

Verified by Experts

The correct Answer is:
(b)
`dy/dx=1/(8sqrt(x)sqrt(9+sqrt(x))sqrt(4+sqrt(9+sqrt(x))))`
`rArr y= sqrt(4+sqrt9+sqrt(x))+c`
Now, `y(0)=sqrt(7)+c`
`rArr c=0`
`y(256)=sqrt(4+sqrt(9+16))=sqrt(4+5)=3`
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