jee-main 2020 Q69

jee-main · India · session2_05sep_shift2 First order differential equations (integrating factor)

Let $y = y(x)$ be the solution of the differential equation $\cos x\frac{dy}{dx} + 2y\sin x = \sin 2x$, $x \in \left(0, \frac{\pi}{2}\right)$. If $y(\pi/3) = 0$, then $y(\pi/4)$ is equal to:
(1) $2 - \sqrt{2}$
(2) $2 + \sqrt{2}$
(3) $\sqrt{2} - 2$
(4) $\frac{1}{\sqrt{2}} - 1$

Let $y = y(x)$ be the solution of the differential equation $\cos x\frac{dy}{dx} + 2y\sin x = \sin 2x$, $x \in \left(0, \frac{\pi}{2}\right)$. If $y(\pi/3) = 0$, then $y(\pi/4)$ is equal to:\\
(1) $2 - \sqrt{2}$\\
(2) $2 + \sqrt{2}$\\
(3) $\sqrt{2} - 2$\\
(4) $\frac{1}{\sqrt{2}} - 1$

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