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Differential Equations question

2025 · 23 Jan · Shift 2 · Q45

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JEE Main
Mathematics
Differential Equations
2025 · 23 Jan · Shift 2 · Q45

Differential Equations question

2025 · 23 Jan · Shift 2 · Q45

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

x=x(y)

be the solution of the differential equation

y=\left(x-y \frac{\mathrm{~d} x}{\mathrm{~d} y}\right) \sin \left(\frac{x}{y}\right), y\gt 0

and

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

. Then

\cos (x(2))

is equal to :

A
$2\left(\log _e 2\right)-1$
B
$1-2\left(\log _e 2\right)^2$
C
$1-2\left(\log _{\mathrm{e}} 2\right)$
D
$2\left(\log _e 2\right)^2-1$

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