If d y d x + 3 cos 2 x y = 1 cos 2 x , x ∈ - π 3 , π 3 , and y π 4 = 4 3 , then y - π 4 equals

Step-by-step solution

Given d y d x + 3 sec 2 x y = sec 2 x This is linear differential equation, of the type d y d x + P y = Q , where P   &   Q are functions of x or constants. Here, P = 3 s e c 2 x   &   Q = s e c 2 x Now, integrating factor I . F . = e ∫ P d x = e ∫ 3 sec 2 x   d x = e 3 tan x Hence, the solution of the differential equation is y I . F . = ∫ Q I . F . d x + c ⇒ y · e 3 tan x = ∫ e 3 tan x · sec 2 x d x Let, tan x = t ,     ⇒ s e