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Differential Equations question

2022 · 28 Jun · Shift 1 · Q31

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JEE Main
Mathematics
Differential Equations
2022 · 28 Jun · Shift 1 · Q31

Differential Equations question

2022 · 28 Jun · Shift 1 · Q31

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let the solution curve

y = y(x)

of the differential equation

\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y

pass through the points (1, 0) and (2

\alpha

,

\alpha

),

\alpha

> 0. Then

\alpha

is equal to

A
${1 \over 2}\exp \left( {{\pi \over 6} + \sqrt e - 1} \right)$
B
${1 \over 2}\exp \left( {{\pi \over 6} + e - 1} \right)$
C
$\exp \left( {{\pi \over 6} + \sqrt e + 1} \right)$
D
$2\exp \left( {{\pi \over 3} + \sqrt e - 1} \right)$

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