Mathematics

Mathematics

Problem

Let y=y(x)y=y(x) be the solution of the differential equation sec⁡2x dx+(e2ytan⁡2x+tan⁡x) dy=0\sec^2 x\,dx + (e^{2y}\tan^2 x + \tan x)\,dy = 0, 0<x<π20 < x < \frac{\pi}{2}, y(π4)=0y\left(\frac{\pi}{4}\right)=0. If y(π6)=αy\left(\frac{\pi}{6}\right)=\alpha, then e8αe^{8\alpha} is equal to _____. ![](![Bookmark icon](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260106T182719Z/2203b549a10644b986674369fd9fcdab/30a26f2d17ca95672702bf50fb4f0242_img.jpg))

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