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Differential Equations

JEE Main 2021 (Online) 25th July Morning Shift

INTEGER+4 / -12021
Let y = y(x) be solution of the following differential equation \({e^y}{{dy} \over {dx}} - 2{e^y}\sin x + \sin x{\cos ^2}x = 0,y\left( {{\pi \over 2}} \right) = 0\) If \(y(0) = {\log _e}(\alpha + \beta {e^{ - 2}})\), then \(4(\alpha + \beta )\) is equal to ______________.

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