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COMEDK2012MathematicsDifferential Equations

The solution of d y d x -1=e^ x-y is

Options

  1. Ae^ x-y +x=c
  2. Be^ -(x-y) +x=c
  3. Ce^ -(x-y) =x+c
  4. De^ x-y =x+c

Correct answer

C. e^ -(x-y) =x+c

Step-by-step solution

Given, differential equation is d y d x -1=e^ x-y array lrl Put & & x-y=t & 1- d y d x = d t d x array So, given equation becomes, aligned - d t d x &=e^ t -e^ -t d t &=d x aligned Integrating both sides, we get aligned &e^ -t =x+c &e^ -(x-y) =x+c aligned

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