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AP EAMCET2007MathematicsDifferential Equations

The differential equation obtained by eliminating the arbitrary constants a and b from x y=a e^x+b e^ -x is

Options

  1. Ax d^2 y d x^2 +2 d y d x -x y=0
  2. Bd^2 y d x^2 +2 y d y d x -x y=0
  3. Cx d^2 y d x^2 +2 d y d x +x y=0
  4. Dd^2 y d x^2 + d y d x -x y=0

Correct answer

A. x d^2 y d x^2 +2 d y d x -x y=0

Step-by-step solution

Given, x y=a e^x+b e^ -x On differentiating w.r.t. x , two times aligned & x d y d x +y=a e^x-b e^ -x & x d^2 y d x^2 + d y d x + d y d x =a e^x+b e^ -x & x d^2 y d x^2 +2 d y d x =x y & x d^2 y d x^2 +2 d y d x -x y=0 aligned

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