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NDA2021MathematicsDifferential EquationsActual

What is the solution of the following differential equation? ( d y d x )+y=x

Options

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

Correct answer

C. e^x-e^y=c

Step-by-step solution

( d y d x )=x-y aligned & e^ x-y = d y d x & e^x d x=e^y d y aligned On integrating both sides, we get, e^x d x= e^y d y aligned & e^x=e^y+c & e^x-e^y=c aligned

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