If y=y(x) satisfies the differential equation 8√x(√9+√x)dy = (√4+√9+√x)dx, x>0 and y(0)=√7, then y(256)___.

8dy = dx√x(√9+√x)(√4+√9+√x)
Let 9+√x = t² ⇒ 1/(2√x)dx = 2tdt ⇒ dx/√x = 4tdt
⇒ 8dy = 4tdt/(t√4+t)
⇒ 2dy = dt/(√4+t)
Integrate both sides
⇒ ∫2dy = ∫dt/(√4+t)
⇒ 2y = 2√4+t + c₁
⇒ y = √4+t + C
Resubstituting the value of t,
⇒ y = √4+√9+√x + C
Now, for x=0, we have y=√7
⇒ √7 = √4+√9+0 + C
⇒ √7 = √7 + C
⇒ C = 0
Hence, the solution of the given differential equation is y = √4+√9+√x
Now, for x=256
y = √4+√9+√256
⇒ y = √4+√9+16
⇒ y = √4+√25
⇒ y = √4+5 = √9 = 3
∴ y(256) = 3
Hence, option C is correct.