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Differential Equations: JEE Mains 2022, June 28 - Shift 1

Hard· Homogeneous equations· +4 / −1

Let

y=y(x)

satisfy the differential equation

x\left(\frac{x}{\sqrt{x^2-y^2}}+e^{y/x}\right)\frac{dy}{dx}=x+y\left(\frac{x}{\sqrt{x^2-y^2}}+e^{y/x}\right)

such that

y(1)=0

. If

y(2\alpha)=\alpha

, find

\alpha

.

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