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Differential Equations question

2025 · 4 Apr · Shift 2 · Q32

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JEE Main
Mathematics
Differential Equations
2025 · 4 Apr · Shift 2 · Q32

Differential Equations question

2025 · 4 Apr · Shift 2 · Q32

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

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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