Let x = x(y) be the solution of the differential equation y = (x - y dx/dy) sin (x/y), y > 0 and x(1) = (π)/2. Then cos (x(2)) is equal to:

Differential Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q237

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

Let

x = x(y)

be the solution of the differential equation

y = \left(x - y \frac{dx}{dy}\right) \sin \left(\frac{x}{y}\right)

y > 0

and

x(1) = \frac{\pi}{2}

. Then

\cos (x(2))

is equal to:

JEE Main 2025 · January, Unspecified (session-level dataset) · Q237

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

Let

x = x(y)

be the solution of the differential equation

y = \left(x - y \frac{dx}{dy}\right) \sin \left(\frac{x}{y}\right)

y > 0

and

x(1) = \frac{\pi}{2}

. Then

\cos (x(2))

is equal to: