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Differential Equations question

2025 · 29 Jan · Shift 2 · Q38

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JEE Main
Mathematics
Differential Equations
2025 · 29 Jan · Shift 2 · Q38

Differential Equations question

2025 · 29 Jan · Shift 2 · Q38

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If for the solution curve

y=f(x)

of the differential equation

\frac{d y}{d x}+(\tan x) y=\frac{2+\sec x}{(1+2 \sec x)^2}

,

x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right), f\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{10}

, then

f\left(\frac{\pi}{4}\right)

is equal to:

A
$\frac{5-\sqrt{3}}{2 \sqrt{2}}$
B
$\frac{4 - \sqrt{2}}{14}$
C
$\frac{9\sqrt{3} + 3}{10(4 + \sqrt{3})}$
D
$\frac{\sqrt{3} + 1}{10(4 + \sqrt{3})}$

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