QJEEAdv17Mac741: JEE Advanced 2017 Mathematics - Class 12 JEEAdv17Mac741 Solution: If y = y(x) satisfies the differential equation dx, x > 0 and…

Question

Verified Solution • 2025–26 Session moderate

If y = y(x) satisfies the differential equation

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

dx, x > 0 and y(0) =

\sqrt 7

, then y(256) =

Accepted Answer

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

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

Now,

y(0) = \sqrt 7 + c

\Rightarrow c = 0

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

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