JEE Math Practice 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 :
- A.$\frac{2 \mathrm{e}^2+\mathrm{e}}{64}$
- B.$\frac{2 \mathrm{e}^2-\mathrm{e}}{64}$
- C.$\frac{2 \mathrm{e}^2-\mathrm{e}}{128}$
- D.$\frac{2 \mathrm{e}^2+\mathrm{e}}{128}$
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