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JEE Main20206 Sep 2020Evening ShiftMathematicsDifferential EquationsActual

If y = 2 π x - 1 cosec x is the solution of the differential equation, d y d x + p x y = - 2 π cosec x , 0 < x < π 2 , then the function p x is equal to :

Options

  1. Acot x
  2. Bcosec x
  3. Csec x
  4. Dtan x

Correct answer

A. cot x

Step-by-step solution

y = 2 π x - 1 cosec   x ⇒ d y d x = 2 π cosec   x - 2 x π - 1 cosec x   cot x cot ⁡ x ⇒ d y d x + 2 x π - 1 cosec x   cot x = 2 π cosec x ⇒ d y d x + y cot x = 2 π cosec x ⇒ p x = cot x

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