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((-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} \cdot y \cdot \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} \cdot y \cdot \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^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((-3/(e^x)-1/(e^{3x)}+c_{1})/(3e))+1