Let {y}={y}({x}) be solution of the following differential equation{e}^{y} {{dy}}/{{dx}}-2 {e}^{y} \sin {x}+\sin {x} \cos ^{2} {x}=0, {y}(\frac{\\pi}{2})=0 If {y}(0)=\log _{e}(\\alpha+\\beta{e}^{-2}), then 4(\\alpha+\\beta) is equal to ________. [25 Jul 2021 Shift 1]

Differential Equations Part 1

Section: Mathematics

Question : 16 of 100

Marks: +1, -0

Let y=y(x) be solution of the following differential equationey

−2ey‌sin‌x+sin‌x‌cos2‌x=0,y(

)=0 If y(0)=loge(α+βe−2), then 4(α+β) is equal to ________.

[25 Jul 2021 Shift 1]

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