If 2 + cos ⁡ x 3 + y d y d x + sin ⁡ x = 0 and y 0 = 1 , then y π 3 is equal to

Question

If 2 + cos ⁡ x 3 + y d y d x + sin ⁡ x = 0 and y 0 = 1 , then y π 3 is equal to, 4 3, 7 3, 1 3, 1

MARKS App · Accepted Answer

d y y + 3 = - sin ⁡ x 2 + cos ⁡ x d x ⇒ ln ⁡ y + 3 = ln ⁡ 2 + cos ⁡ x + ln ⁡ C ⇒ y + 3 = C ( 2 + cos ⁡ x ) Now, at x = 0 , y = 1 ⇒ 4 = 3 C ⇒ C = 4 3 ⇒ y = 4 3 2 + cos ⁡ x - 3 Hence, y π 3 = 4 3 2 + 1 2 − 3 = 2 3 ⋅ 5 − 3 = 1 3

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