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JEE Main20199 Jan 2019Morning ShiftMathematicsDifferential EquationsActual

If y = y ( x ) is the solution of the differential equation, x d y d x + 2 y = x 2 satisfying y 1 = 1 , then y 1 2 is equal to

Options

  1. A7 64
  2. B1 4
  3. C13 16
  4. D49 16

Correct answer

D. 49 16

Step-by-step solution

Given differential equation can be written as d y d x + 2 y x = x , which is a linear differential equation. If = e ∫ 2 x d x = e 2   l n   x = x 2 Solution is y . x 2 = ∫ x . x 2 d x ⇒ y . x 2 = x 4 4 + c Since, given curve passes through 1 , 1 ⇒ c = 3 4 Hence, y x = x 2 4 + 3 4 x 2 . So, y 1 2 = 49 16 .

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