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Differential Equations question

2024 · 31 Jan · Shift 2 · Q52

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JEE Main
Mathematics
Differential Equations
2024 · 31 Jan · Shift 2 · Q52

Differential Equations question

2024 · 31 Jan · Shift 2 · Q52

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=y(x)

be the solution of the differential equation

\sec ^2 x d x+\left(e^{2 y} \tan ^2 x+\tan x\right) d y=0,0\lt x\lt \frac{\pi}{2}, y(\pi / 4)=0

. If

y(\pi / 6)=\alpha

, then

e^{8 \alpha}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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