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JEE Main2017MathematicsDifferentiationActual

If 2 x = y 1 5 + y - 1 5 and x 2 - 1 d 2 y d x 2 + λ x d y d x + k y = 0 , then λ + k is equal to

Options

  1. A26
  2. B- 24
  3. C- 23
  4. D- 26

Correct answer

B. - 24

Step-by-step solution

Given y 1 5 + y - 1 5 = 2 x ⇒ 1 5 y - 4 5 - 1 5 y - 6 5 d y d x = 2   ⇒ y ′ y 1 5 - y - 1 5 = 10 y ⇒ y ′   2 x 2 - 1 = 10 y ⇒ y ′   x 2 - 1 = 5 y Differentiating again y ′ ′ 2 x 2 - 1 + y ′ 2 2 x 2 x 2 - 1 =10y' ⇒ y ′ ′ x 2 - 1 + x y ′ = 5 x 2 - 1   y ′ ⇒ y ′ ′   x 2 - 1 + x y ′ - 25 y = 0 ⇒ λ = 1 ,   k = - 25

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