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Differential Equations question

2023 · 6 Apr · Shift 1 · Q36

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JEE Main
Mathematics
Differential Equations
2023 · 6 Apr · Shift 1 · Q36

Differential Equations question

2023 · 6 Apr · Shift 1 · Q36

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=y(x)

be a solution of the differential equation

(x \cos x) d y+(x y \sin x+y \cos x-1) d x=0,0 \lt x \lt \frac{\pi}{2}

. If

\frac{\pi}{3} y\left(\frac{\pi}{3}\right)=\sqrt{3}

, then

\left|\frac{\pi}{6} y^{\prime \prime}\left(\frac{\pi}{6}\right)+2 y^{\prime}\left(\frac{\pi}{6}\right)\right|

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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