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Differential Equations question

2022 · 26 Jul · Shift 2 · Q28

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JEE Main
Mathematics
Differential Equations
2022 · 26 Jul · Shift 2 · Q28

Differential Equations question

2022 · 26 Jul · Shift 2 · Q28

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let the solution curve

y=f(x)

of the differential equation

\frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{4}+2 x}{\sqrt{1-x^{2}}}

,

x\in(-1,1)

pass through the origin. Then

\int\limits_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) d x

is equal to

A
$\frac{\pi}{3}-\frac{1}{4}$
B
$\frac{\pi}{3}-\frac{\sqrt{3}}{4}$
C
$\frac{\pi}{6}-\frac{\sqrt{3}}{4}$
D
$\frac{\pi}{6}-\frac{\sqrt{3}}{2}$

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