If a curve y=y(x) passes through the point (1,(π)/2) and satisfies the differential equation (7x⁴ cot y - eˣ csc y)dx/dy = x⁵, x≥1, then at x=2, the value of cos y is:

Differential Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q116

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumDifferential Equations163× since 2002

If a curve

y=y(x)

passes through the point

(1,\tfrac{\pi}{2})

and satisfies the differential equation

\bigl(7x^4\cot y - e^x\csc y\bigr)\frac{dx}{dy} = x^5

x\ge1

, then at

x=2

, the value of

\cos y

is: