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AP EAMCET202119 Aug 2021Evening ShiftMathematicsDifferential EquationsActual

If x 2 + y 2 = 1 , then

Options

  1. Ay y ′ ′ - 2 y ′ 2 + 1 = 0
  2. By y ′ ′ + y ′ 2 + 1 = 0
  3. Cy y ′ ′ - y ′ 2 - 1 = 0
  4. Dy y ′ ′ + 2 y ′ 2 + 1 = 0

Correct answer

B. y y ′ ′ + y ′ 2 + 1 = 0

Step-by-step solution

Given, x 2 + y 2 = 1 On differentiating w.r.t. x , we get 2 x + 2 y y ' = 0 ⇒   x + y y ' = 0 Again, differentiating, we get 1 + y y '' + y ' 2 = 0

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