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Question 141 of 490MediumNUMERICAL
Let y=y(x)y=y(x) solve sec⁡2x dx+(e2ytan⁡2x+tan⁡x) dy=0\sec^2x\,dx+(e^{2y}\tan2x+\tan x)\,dy=0, 0<x<π20<x<\dfrac{\pi}{2}, y(π4)=0y\left(\dfrac{\pi}{4}\right)=0. If y(π6)=αy\left(\dfrac{\pi}{6}\right)=\alpha, then e8αe^{8\alpha} is equal to \_\_\_\_\_\_. Answer: 9
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