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JEE Main20202 Sep 2020Morning ShiftMathematicsDifferential EquationsActual

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

Options

  1. A2 ,   3 2
  2. B1 ,   − 1
  3. C1 ,   1
  4. D2 ,   1

Correct answer

C. 1 ,   1

Step-by-step solution

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    ⇒    y = 4 2 + sin x - 1 y π = 2 - 1 = 1 = a d y d x = - 4 2 + sin x 2 · cos x = 1 At   x = π ⇒ b = 1 a , b = 1 , 1

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