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Differential Equations question

2025 · 22 Jan · Shift 2 · Q32

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JEE Main
Mathematics
Differential Equations
2025 · 22 Jan · Shift 2 · Q32

Differential Equations question

2025 · 22 Jan · Shift 2 · Q32

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If

x=f(y)

is the solution of the differential equation

\left(1+y^2\right)+\left(x-2 \mathrm{e}^{\tan ^{-1} y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=0, y \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

with

f(0)=1

, then

f\left(\frac{1}{\sqrt{3}}\right)

is equal to :

A
$\mathrm{e}^{\pi / 4}$
B
$e^{\pi / 12}$
C
$\mathrm{e}^{\pi / 6}$
D
$e^{\pi / 3}$

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