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Differential Equations question

2025 · 22 Jan · Shift 2 · Q47

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JEE Main
Mathematics
Differential Equations
2025 · 22 Jan · Shift 2 · Q47

Differential Equations question

2025 · 22 Jan · Shift 2 · Q47

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=f(x)

be the solution of the differential equation

\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{x y}{x^2-1}=\frac{x^6+4 x}{\sqrt{1-x^2}},-1\lt x\lt 1

such that

f(0)=0

. If

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

then

\alpha^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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