Let the solution curve y=y(x) of the differential equation [\frac{x}\sqrt{x^2-y^2}+e^{\frac{y}{x}}] x \frac{d y}{d x}=x+[\frac{x}\sqrt{x^2-y^2}+e^{\frac{y}{x}}] y pass through the points (1,0) and (2 \alpha, \alpha), \alpha>0. Then \alpha is equal to [28-Jun-2022-Shift-1]

Correct Answer is : 12exp(π6+√e−1)

\frac{1}{2} \exp (\frac{\pi}{6}+\sqrt{e}-1)

\frac{1}{2} \exp (\frac{\pi}{6}+e-1)

\exp (\frac{\pi}{6}+\sqrt{e}+1)

2 \exp (\frac{\pi}{3}+\sqrt{e}-1)

Differential Equations Part 2

Section: Mathematics

Question : 83 of 100

Marks: +1, -0

Let the solution curve y=y(x) of the differential equation
[‌

√x2−y2

+e‌

]x‌

=x+[‌

√x2−y2

+e‌

]y
pass through the points (1,0) and (2α,α),α>0. Then α is equal to

[28-Jun-2022-Shift-1]

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