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AP EAMCET202119 Aug 2021Morning ShiftMathematicsDifferentiationActual

If y = x + 1 x , then which among the following holds?

Options

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

Correct answer

C. x 2 y ' − x y + 2 = 0

Step-by-step solution

Given that y   =   x   +   1 x Differentiate with respect to x d y d x   =   1   - 1 x 2 ⇒ y '   =   x 2 - 1 x 2 ⇒ x 2 y '   =   x 2 - 1 ⇒ x 2 y '   - x 2 + 1 = 0 ⇒ x 2 y '   -   x x - 1 x = 0 ⇒ x 2 y '   -   x x + 1 x + 2 = 0 ⇒ x 2 y '   - x y + 2 = 0

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