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Differential Equations question

2025 · 28 Jan · Shift 2 · Q48

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JEE Main
Mathematics
Differential Equations
2025 · 28 Jan · Shift 2 · Q48

Differential Equations question

2025 · 28 Jan · Shift 2 · Q48

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

If

y=y(x)

is the solution of the differential equation,

\sqrt{4-x^2} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\left(\left(\sin ^{-1}\left(\frac{x}{2}\right)\right)^2-y\right) \sin ^{-1}\left(\frac{x}{2}\right),-2 \leq x \leq 2, y(2)=\frac{\pi^2-8}{4}

, then

y^2(0)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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