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