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AP EAMCET202124 Aug 2021Morning ShiftMathematicsDifferential EquationsActual

Solve the differential equation : d y d x =e^ x+y

Options

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

Correct answer

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

Step-by-step solution

aligned d y d x & =e^ x+y d y d x & =e^x e^y d y e^y =e^x d x e^ -y d y & =e^x d x aligned Integrating both sides, aligned & e^ -y d y= e^x d x & e^ -y -1 =e^x+c e^x+e^ -y +c=0 & e^x+e^ -y =-c e^x+e^ -y =c & aligned when c=-c

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