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

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

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e^{-x}y(dy)/(dx)=e^{-y}+e^{-2x-y}

e^{- x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

y = W (\frac{2 sinh ( x ) + c _{1}}{e}) + 1

Solution steps

e^{- x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

Solve separable ODE:

y = W (\frac{2 sinh ( x ) + c _{1}}{e}) + 1

y = W (\frac{2 sinh ( x ) + c _{1}}{e}) + 1

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