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

Step-by-step solution

We have, 2 + sin x d y d x = - y + 1 cos x ⇒ ∫ d y y + 1 = - ∫ cos x sin x + 2 d x Let, sin x = t ⇒ cos x d x = d t ⇒ log y + 1 = - ∫ d t t + 2 + C where, C is the constant of integration. ⇒ log y + 1 + log sin x + 2 - C = 0 ⇒ log y + 1 sin x + 2 = C Given, y 0 = 1 ⇒ C = log 4 . ⇒ log y + 1 sin x + 2 = log 4         . . . . . i Now, put x = π 2 in the equation i , we get, log y + 1 + log 3 - log 4 = 0 ⇒  log y + 1 = log