Discussion Forum

1)

if y=y(x) satisfies the differential equation

$8\sqrt{x}(\sqrt{9+\sqrt{x}})dy=(\sqrt{4+\sqrt{9+\sqrt{x}}})^{-1}$

dx,x >0 and $y(0)=\sqrt{7}$ , then y(256)=

Answer:

Option B

Explanation:

$\frac{dy}{dx}= \frac{1}{8\sqrt{x}\sqrt{9+\sqrt{x}}\sqrt{4+\sqrt{9+\sqrt{x}}}}$

$\Rightarrow y=\sqrt{4+\sqrt{9+\sqrt{x}}}+c$

Now, y(0)=$\sqrt{7}+c$

  c=0

$y(256)=\sqrt{4+\sqrt{9+16}}=\sqrt{4+5}=3$