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AP EAMCET2007MathematicsDifferential Equations

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

Options

  1. Ae^ -(x+y) +x+c=0
  2. Be^ -(x+y) -x+c=0
  3. Ce^ x+y +x+c=0
  4. De^ x+y -x+c=0

Correct answer

A. e^ -(x+y) +x+c=0

Step-by-step solution

Given, d y d x +1=e^ x+y Put x+y=z aligned & & 1+ d y d x & = d z d x & & d z d x & =e^z & & e^ -z d z & = d x & & -e^ -z & =x+c & & -e^ -(x+y) & =x+c & & x+e^ -(x+y) +c & =0 aligned

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