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

The solution for -e^xy(dy)/(dx)=e^{-y}+e^{-2x-y} is y=\W((3/(e^x)+1/(e^{3x)}+c_{1})/(3e))+1

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

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

y = W (\frac{\frac{3}{e ^{x}} + \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

Solution steps

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

Solve separable ODE:

y = W (\frac{\frac{3}{e ^{x}} + \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

y = W (\frac{\frac{3}{e ^{x}} + \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

What is the solution for -e^xy(dy)/(dx)=e^{-y}+e^{-2x-y} ?
The solution for -e^xy(dy)/(dx)=e^{-y}+e^{-2x-y} is y=\W((3/(e^x)+1/(e^{3x)}+c_{1})/(3e))+1