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Differential Equations question

2021 · 20 Jul · Shift 1 · Q29

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JEE Main
Mathematics
Differential Equations
2021 · 20 Jul · Shift 1 · Q29

Differential Equations question

2021 · 20 Jul · Shift 1 · Q29

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let y = y(x) be the solution of the differential equation

x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( {{y \over x}} \right) - x} \right)dx

,

- 1 \le x \le 1

,

y\left( {{1 \over 2}} \right) = {\pi \over 6}

. Then the area of the region bounded by the curves x = 0,

x = {1 \over {\sqrt 2 }}

and y = y(x) in the upper half plane is :

A
${1 \over 8}(\pi - 1)$
B
${1 \over {12}}(\pi - 3)$
C
${1 \over 4}(\pi - 2)$
D
${1 \over 6}(\pi - 1)$

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