Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x ∈ 0 , π 2 If y ( π / 3 ) = 0 , then y ( π / 4 ) is equal to :

Question

Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x &#8712; 0 , &#960; 2 If y ( &#960; / 3 ) = 0 , then y ( &#960; / 4 ) is equal to :

Aicharya · Accepted Answer

d y d x + 2 tan x &#183; y = 2 sin x I.F. = e &#8747; 2 tan x d x = sec 2 x solution is y &#183; sec 2 x = &#8747; 2 sin x &#183; sec 2 x d x + C y sec 2 x = 2 sec x + C &#8658; 0 = 2 . 2 + C &#8658; C = - 4 y sec 2 x = 2 sec x - 4 y &#960; 4 = 2 - 2

Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x ∈…

Solution

Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x &#8712;…

Solution

Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x ∈…