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MCQMediumJEE Main 2025 · 22 January, Shift 2Linear Differential Equations

Mathematics Question from JEE Main 2025 · 22 January, Shift 2

If x=f(y)x = f(y) is the solution of the differential equation

(1+y2)+(x−2etan⁡−1y)dydx=0,y∈(−π2,π2),(1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right),

with f(0)=1f(0) = 1, then f(13)f\left( \frac{1}{\sqrt{3}} \right) is equal to:

  • A

    eπ3e^{\frac{\pi}{3}}

  • B

    eπ12e^{\frac{\pi}{12}}

  • C

    eπ6e^{\frac{\pi}{6}}

  • D

    eπ4e^{\frac{\pi}{4}}

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