If d y d x + y tan x = sin 2 x and y 0 = 1 , then y π is equal to

Step-by-step solution

The given differential equation d y d x + y tan x = sin 2 x is linear differential equation of the form d y d x + P x y = Q x with P ( x ) = tan x , Q ( x ) = sin 2 x Now, I . F . = e ∫ P x d x = e ∫ tan x dx = e ln sec x = sec x And, the solution is y I . F . = ∫ Q x I . F . d x + c ⇒ y sec x = ∫ sec x sin 2 x d x + c ⇒ y sec x = ∫ 1 cos x 2 sin x cos x d x + c ⇒ y sec x = ∫ 2 sin x d x + c ⇒ y sec x = - 2 cos x + c Given, y 0 = 1 ⇒ 1 · sec 0 =