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NVAMediumJEE Main 2025 · 22 January, Shift 2Linear Differential Equations

Mathematics Question from JEE Main 2025 · 22 January, Shift 2

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

dydx+xyx2−1=x6+4x1−x2,−1<x<1\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1

such that f(0)=0f(0) = 0. If

6∫−1/21/2f(x)dx=2π−α6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha

then α2\alpha^2 is equal to _____.

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