Let y = y(x) be a solution of the differential equation (xcos x)… | JEE Main 2023 Mathematics PYQ

NVAMediumJEE Main 2023 · 6 April, Shift 1Linear Differential Equations

Let $y = y(x)$ be a solution of the differential equation $(x\cos x)\,dy + (xy\sin x + y\cos x - 1)\,dx = 0$ , $0 < x < \frac{\pi}{2}$ . If $\frac{\pi}{3}\,y\!\left(\frac{\pi}{3}\right) = \sqrt{3}$ , then $\left|\frac{\pi}{6}\,y''\!\left(\frac{\pi}{6}\right) + 2y'\!\left(\frac{\pi}{6}\right)\right|$ is equal to:

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