Let y = y x be the solution of the differential equation sin ⁡ x d y d x + y cos x ⁡ = 4 x ,   x ∈ 0 ,   π . If y π 2 = 0 , then y π 6 is equal to

Question

Let y = y x be the solution of the differential equation sin &#8289; x d y d x + y cos x &#8289; = 4 x , &#160; x &#8712; 0 , &#160; &#960; . If y &#960; 2 = 0 , then y &#960; 6 is equal to

Aicharya · Accepted Answer

d y d x + y cot &#160; x = 4 x sin x , &#160; x &#8712; 0 , &#160; &#960; I.F. = e &#8747; cot x = e ln &#8289; sin x = sin x &#8756; y &#160; sin x = &#8747; 4 x sin x . sin x &#160; d x y sin x = 2 x 2 + c &#8757; y &#960; 2 = 0 &#8756; 0 &#215; 1 = 2 &#215; &#960; 2 2 + c &#8658; c = - &#960; 2 2 y &#960; 6 = 2 &#215; &#960; 6 2 - &#960; 2 2 1 2 = &#960; 2 18 - &#960; 2 2 &#215; 2 = &#960; 2 9 - &#960; 2 = - 8 &#960; 2 9

Let y = y x be the solution of the differential equation sin ⁡ x d y d x + y cos x ⁡ = 4 x ,…

Solution

Let y = y x be the solution of the differential equation sin &#8289; x d y d x + y cos x &#8289; = 4 x ,…

Solution

Let y = y x be the solution of the differential equation sin ⁡ x d y d x + y cos x ⁡ = 4 x ,…