If y = y x is the solution of the differential equation d y d x + tan x y = sin x , 0 ≤ x ≤ π 3 , with y 0 = 0 , then y π 4 is equal to

Step-by-step solution

d y d x + tan x y = sin x ;   0 ≤ x ≤ π 3 I . F . = e ∫ tan x d x = e ln sec x = sec x y sec x = ∫ tan x d x + C y sec x = ln sec x + C x = 0 ,   y = 0    ⇒   C = 0 y sec x = ln sec x y = cos x · ln sec x y x = π 4 = 1 2 · ln 2 y x = π 4 = 1 2 2 log e 2