What is the solution for (dy)/(dx)e^{x+y}=x+1 ?

The solution for (dy)/(dx)e^{x+y}=x+1 is y=ln(-xe^{-x}-2e^{-x}+c_{1})

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(dy)/(dx)e^{x+y}=x+1

\frac{d y}{d x} e^{x + y} = x + 1

y = ln (- x e^{- x} - 2 e^{- x} + c_{1})

Solution steps

\frac{d y}{d x} e^{x + y} = x + 1

Solve separable ODE:

y = ln (- x e^{- x} - 2 e^{- x} + c_{1})

y = ln (- x e^{- x} - 2 e^{- x} + c_{1})

\frac{d y}{d x} = e^{x} (1 - y)^{2}

y^{^{'}} = sin (3 y)

\frac{d y}{d x} = e^{5 y} cos (\frac{x}{2})

(x^{2} - 3) \frac{d y}{d x} - x (y - 1) = 0

x + 3 y^{2} x^{2} + 1 \frac{d y}{d x} = 0

What is the solution for (dy)/(dx)e^{x+y}=x+1 ?
The solution for (dy)/(dx)e^{x+y}=x+1 is y=ln(-xe^{-x}-2e^{-x}+c_{1})