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JEE Main202227 Jun 2022Morning ShiftMathematicsDifferentiationActual

If cos - 1 y 2 = log e x 5 5 , y < 2 , then

Options

  1. Ax 2 y '' + x y ' - 25 y = 0
  2. Bx 2 y '' - x y ' - 25 y = 0
  3. Cx 2 y '' - x y ' + 25 y = 0
  4. Dx 2 y '' + x y ' + 25 y = 0

Correct answer

D. x 2 y '' + x y ' + 25 y = 0

Step-by-step solution

Given, cos - 1 y 2 = log e x 5 5 Using property log x m = m log x we get, cos - 1 y 2 = 5 log e x 5 Now differentiating both side w.r.t x we get, - 1 1 - y 2 4 · y ' 2 = 5 · 1 x 5 · 1 5 ⇒ - y ' 4 - y 2 = 5 x ⇒ - x y ' = 5 4 - y 2 Again differentiating w.r.t x we get, ⇒ - x y '' - y ' = 5 · 1 2 4 - y 2 - 2 y y ' ⇒ x y '' + y ' = 5 y y ' 4 - y 2 ⇒ x y '' + y ' = 5 y · - 5 x ⇒ x 2 y '' + x y ' = - 25 y ⇒ x 2 y &#

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