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Differential Equations: JEE Mains 2022 June 29 Shift 1

Hard· Linear differential equations· +4 / 0

Let

y=y(x)

be the solution of the differential equation

\frac{dy}{dx}+\frac{\sqrt2\,y}{2\cos^4x-\cos2x}=x\,e^{\tan^{-1}(\sqrt2\cot2x)},\quad 0<x<\frac\pi2

with

y\left(\dfrac\pi4\right)=\dfrac{\pi^2}{32}

. If

y\left(\dfrac\pi3\right)=\dfrac{\pi^2}{18}e^{-\tan^{-1}(\alpha)}

, then the value of

3\alpha^2

is equal to ______.

Your answer (numerical)

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