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Manipal MET2012MathematicsDifferential Equations

The solution of differential equation (e^x+1 ) y d y=(y+1) e^x d x is

Options

  1. A(e^x+1 )(y+1)=C e^y
  2. B(e^x+1 )|(y+1)|=C e^ -y
  3. C(e^x+1 )(y+1)= C e^y
  4. DNone of the above

Correct answer

A. (e^x+1 )(y+1)=C e^y

Step-by-step solution

The given differential equation is aligned & (e^x+1 ) y d y= & y d y (y+1) = e^x (e^x+1 ) d x & ( y+1-1 y+1 ) d y= e^x e^x+1 d x & d y- 1 y+1 d y= e^x e^x+1 d x aligned On integrating, we get array cc & y- |y+1| & (e^x+1 )+ k & y= |(y+1) (e^x+1 ) | k & (y+1) (e^x+1 )=e^y C array

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