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JEE Main20199 Apr 2019Evening ShiftMathematicsDifferential EquationsActual

If c o s x d y d x - y s i n x = 6 x , 0 < x < π 2 and y π 3 = 0 , then y π 6 is equal to

Options

  1. A- π 2 4 3
  2. Bπ 2 2 3
  3. C- π 2 2
  4. D- π 2 2 3

Correct answer

D. - π 2 2 3

Step-by-step solution

The given D . E . can be written as d y d x - y tan x = 6 x sec x       . . . i , which is a liner differential equation of the form d y d x + P y = Q , where P   &   Q are the function of x or constants. Here, P = - tan x   &   Q = 6 x s e c x Integrating factor = e ∫ P d x = e - ∫ tan x   d x = e - - ln cos x = e ln cos x = cos x And, the solution of the linear differential equation is, y I . F . = ∫ Q I . F . d x + c ⇒ y ⋅ cos x = &#

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