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

x=t2,dydx=dydt·dtdxdxdt=2i⇒dydx=12t·dydtdydt=124+9+t.129+ty=4+9+ty=4+9+x+cy0=7 ⇒ c=0y256 = 4+9+164+5=3

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

x=t2,dydx=dydt·dtdxdxdt=2i⇒dydx=12t·dydtdydt=124+9+t.129+ty=4+9+ty=4+9+x+cy0=7 ⇒ c=0y256 = 4+9+164+5=3

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$If y = y (x) satisfies the differential equation 8 \sqrt{x} (\sqrt{9 + \sqrt{x}}) d y = (\sqrt{4 + \sqrt{9 + \sqrt{x}}})^{- 1} d x, x > 0 and$ $y (0) = \sqrt{7} then y (256) =$

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$x = t^{2}, \frac{d y}{d x} = \frac{d y}{d t} \cdot \frac{d t}{d x}$

$\frac{d x}{d t} = 2 i \Rightarrow \frac{d y}{d x} = \frac{1}{2 t} \cdot \frac{d y}{d t}$

$\frac{d y}{d t} = \frac{1}{2 \sqrt{4 + \sqrt{9 + t}}} . \frac{1}{2 \sqrt{9 + t}}$

$y = \sqrt{4 + \sqrt{9 + t}}$

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

$\begin{array}{l} y (0) = \sqrt{7} \Rightarrow c = 0 \\ y (256) = \sqrt{4 + \sqrt{9 + 16}} \\ \sqrt{4 + 5} = 3 \end{array}$

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

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$If y = y (x) satisfies the differential equation 8 \sqrt{x} (\sqrt{9 + \sqrt{x}}) d y = (\sqrt{4 + \sqrt{9 + \sqrt{x}}})^{- 1} d x, x > 0 and$ $y (0) = \sqrt{7} then y (256) =$