MathsJEE Main 8 Apr 2026, Shift 2·Q17·MCQ·Moderate

Differential Equations · Linear differential equations

Let

y = y(x)

be the solution of the differential equation

x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0,

x \in (0, 1)

,

\displaystyle\lim_{x\to1^-} y(x) = 1

. Then

y\left(\dfrac12\right)

equals:

(1) $3 - \dfrac{\pi}{\sqrt3}$
(2) $4 - \sqrt3\,\pi$
(3) $4 - \dfrac{2\pi}{\sqrt3}$
(4) $3 - \dfrac{\pi}{2\sqrt3}$

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