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JEE Main20205 Sep 2020Evening ShiftMathematicsDifferential EquationsActual

Let y = y ( x ) be the solution of the differential equation cos x d y d x + 2 y sin x = sin 2 x , x ∈ 0 , π 2 If y ( π / 3 ) = 0 , then y ( π / 4 ) is equal to :

Options

  1. A2 - 2
  2. B2 + 2
  3. C2 - 2
  4. D1 2 - 1

Correct answer

C. 2 - 2

Step-by-step solution

d y d x + 2 tan x · y = 2 sin x I.F. = e ∫ 2 tan x d x = sec 2 x solution is y · sec 2 x = ∫ 2 sin x · sec 2 x d x + C y sec 2 x = 2 sec x + C ⇒ 0 = 2 . 2 + C ⇒ C = - 4 y sec 2 x = 2 sec x - 4 y π 4 = 2 - 2

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