Let y = y x be the solution of the differential equation, 2 + sin x y + 1 . d y d x = − cos x , y > 0 ,   y 0 = 1 . If y π = a and d y d x at x = π is b , then the ordered pair a ,   b is equal to

Question

Let y = y x be the solution of the differential equation, 2 + sin x y + 1 . d y d x = &#8722; cos x , y &#62; 0 , &#160; y 0 = 1 . If y &#960; = a and d y d x at x = &#960; is b , then the ordered pair a , &#160; b is equal to

Aicharya · Accepted Answer

d y 1 + y = - cos x 2 + sin x d x ln 1 + y = - ln 2 + sin x + ln c 1 + y 2 + sin x = c We know y 0 = 1 So c = 4 1 + y = 4 2 + sin x &#160;&#160; &#8658; &#160;&#160; y = 4 2 + sin x - 1 y &#960; = 2 - 1 = 1 = a d y d x = - 4 2 + sin x 2 &#183; cos x = 1 At &#160; x = &#960; &#8658; b = 1 a , b = 1 , 1

Let y = y x be the solution of the differential equation, 2 + sin x y + 1 . d y d x = − cos x , y &#62…

Solution

Let y = y x be the solution of the differential equation, 2 + sin x y + 1 . d y d x = &#8722; cos x , y &#62…

Solution

Let y = y x be the solution of the differential equation, 2 + sin x y + 1 . d y d x = − cos x , y &#62…