If x=f(y) is the solution of the differential equation (1+y²) + (x - 2e^ tan ⁻¹ y) dy/dx = 0, y (-(π)/2, (π)/2) with f(0)=1, then f(1/(√(3))) is equal to:

Differential Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q41

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

x=f(y)

is the solution of the differential equation

\left(1+y^2\right) + \left(x - 2e^{\tan^{-1} y}\right) \frac{dy}{dx} = 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: