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Differential Equations question

2022 · 27 Jul · Shift 1 · Q42

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JEE Main
Mathematics
Differential Equations
2022 · 27 Jul · Shift 1 · Q42

Differential Equations question

2022 · 27 Jul · Shift 1 · Q42

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=y(x)

be the solution curve of the differential equation

\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x^2}} \right)dy + \left( {4xy - 4\sqrt 2 x\sin \left( {{x^2} - {\pi \over 4}} \right)} \right)dx = 0

,

0 \lt x \lt \sqrt {{\pi \over 2}}

, which passes through the point

\left(\sqrt{\frac{\pi}{6}}, 1\right)

. Then

\left|y\left(\sqrt{\frac{\pi}{3}}\right)\right|

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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