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AP EAMCET2012MathematicsDifferential Equations

If d y d x +2 x (x-y)=1 , then (x-y) is equal to

Options

  1. AA e^ -x^2
  2. BA e^ 2 x
  3. CA e^ x^2
  4. DA e^ -2 x

Correct answer

C. A e^ x^2

Step-by-step solution

Given differential equation is d y d x +2 x (x-y)=1 Put x-y=t array lrl & 1- d y d x = d t d x & d y d x =1- d t d x & 1- d t d x +2 x t=1 & d t t =2 x d x & t d t=2 x d x array On integrating both sides, we get aligned t & =x^2+ A (x-y) A & =x^2 (x-y) & =A e^ x^2 aligned

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