If y=y(x) is the solution curve of the differential equation (d y)/(d x)+y tan x=x sec x, 0 ≤ x ≤ (π)/3, y(0)=1, then y((π)/6) is equal to

(D) (π)/12-(√(3))/2 log e (2/(e √(3)))

(A) (π)/12-(√(3))/2 log e ((2 √(3))/e)

(B) (π)/12+(√(3))/2 log e ((2 √(3))/e)

(C) (π)/12+(√(3))/2 log e (2/(e √(3)))

Differential Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Morning shift · Q3553

JEE Main 20231 Feb, Morning shiftMathematicsMediumDifferential Equations163× since 2002

y=y(x)

is the solution curve of the differential equation

\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1

, then

y\left(\frac{\pi}{6}\right)

is equal to

JEE Main 2023 · 1 Feb, Morning shift · Q3553

JEE Main 20231 Feb, Morning shiftMathematicsMediumDifferential Equations163× since 2002

y=y(x)

is the solution curve of the differential equation

\frac{d y}{d x}+y \tan x=x \sec x, 0 \leq x \leq \frac{\pi}{3}, y(0)=1

, then

y\left(\frac{\pi}{6}\right)

is equal to