If for the solution curve y=f(x) of the differential equation dy/dx+(tan x)y=(2+ sec x)/((1+2 sec x)²), x (-(π)/2, (π)/2), f((π)/3)=(√(3))/10, then f((π)/4) is equal to:

Differential Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q128

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

If for the solution curve

y=f(x)

of the differential equation

\frac{dy}{dx}+(\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: