Let y=f(x) be the solution of the differential equation dy/dx + xy/(x²-1) = (x⁴ + 4x)/(√(1-x²)), -1 < x < 1 such that f(0)=0. If 6 ∫ -1/2 ^(1/2) f(x) dx = 2π - α then α² is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q49

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

Let

y=f(x)

be the solution of the differential equation

\frac{dy}{dx} + \frac{xy}{x^2-1} = \frac{x^4 + 4x}{\sqrt{1-x^2}}, -1 < x < 1

such that

f(0)=0

. If

6 \int_{-1/2}^{1/2} f(x) dx = 2\pi - \alpha

then

\alpha^2

is equal to:

Your answerInteger or decimal