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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\int (t - 1) e^{- s t} d t

- y = x y^{^{'}}

x y^{^{'}} + (x + 1) y = 6

(\frac{d y}{d x})^{2} + 2 e^{x} (\frac{d y}{d x}) + e^{2 x} = 0

\frac{\partial}{\partial x} (2 x y e^{x y^{2}})

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