Question:medium
Let $y = y(x)$ be the solution of the differential equation
$(\tan x)^{1/2} dy = (\sec^3 x - (\tan x)^{3/2}) dx, 0 < x < \frac{\pi}{2}, y\left( \frac{\pi}{4} \right) = \frac{6\sqrt{2}}{5}$. If $y\left( \frac{\pi}{3} \right) = \frac{4}{5} \alpha$, then $\alpha^4$ equals :
Let $y = y(x)$ be the solution of the differential equation
$(\tan x)^{1/2} dy = (\sec^3 x - (\tan x)^{3/2}) dx, 0 < x < \frac{\pi}{2}, y\left( \frac{\pi}{4} \right) = \frac{6\sqrt{2}}{5}$. If $y\left( \frac{\pi}{3} \right) = \frac{4}{5} \alpha$, then $\alpha^4$ equals :
Updated On: Apr 12, 2026
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Correct Answer: 27
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