If a curve y=y(x) passes through the point (1,π/2)... | Differential Equations | JEE Main

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JEE MAIN 2025

4-4-2025 S2

Question

If a curve $y=y(x)$ passes through the point $\left(1, \frac{\pi}{2}\right)$ and satisfies the differential equation $\left(7 x^4 \cot y-\mathrm{e}^x \operatorname{cosec} y\right) \frac{\mathrm{d} x}{\mathrm{~d} y}=x^5, x \geq 1$, then at $x=2$, the value of $\cos y$ is :

Select the correct option:

A

$\frac{2 \mathrm{e}^2-\mathrm{e}}{128}$

B

$\frac{2 \mathrm{e}^2-\mathrm{e}}{64}$

C

$\frac{2 \mathrm{e}^2+\mathrm{e}}{128}$

D

$\frac{2 \mathrm{e}^2+\mathrm{e}}{64}$

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