MathsJEE Main 5 Apr 2026, Shift 2·Q25·Numerical·Moderate

Differential Equations · Linear differential equations

Let

y = y(x)

be the solution of the differential equation

(\tan x)^{1/2}\,dy = \left(\sec^3x - (\tan x)^{3/2}y\right)dx,

0 < x < \dfrac{\pi}{2}

,

y\left(\dfrac{\pi}{4}\right) = \dfrac{6\sqrt2}{5}

. If

y\left(\dfrac{\pi}{3}\right) = \dfrac45\alpha

, then

\alpha^4

equals .

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