If y = y ( x ) is the solution of the differential equation d y d x = ( t a n x - y ) s e c 2 x , x ∈ - π 2 , π 2 , such that y 0 = 0 , then y - π 4 is equal to:

Step-by-step solution

The given differential equation can be written as d y d x + y s e c 2 x = t a n x . s e c 2 x Integrating factor = e ∫ s e c 2 x d x = e t a n x Hence, solution of given differential equation, y . e t a n x = ∫ t a n x . s e c 2 x . e t a n x d x ⇒ y . e t a n x = t a n x . e t a n x - ∫ s e c 2 x . e t a n x d x (using integration by parts) ⇒ y . e tan x = tan x . e tan x - e tan x + c Given, y 0 = 0 ⇒ c = 1 Solution of given differential is y . e t a n x = t a n x . e t a n x -