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((-4e^{-3x}+c_{1})/(3e)))/2+1/2

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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 = \frac{W ( \frac{- 4 e ^{- 3 x} + c _{1}}{3 e} )}{2} + \frac{1}{2}

Solution steps

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

Solve separable ODE:

y = \frac{W ( \frac{- 4 e ^{- 3 x} + c _{1}}{3 e} )}{2} + \frac{1}{2}

y = \frac{W ( \frac{- 4 e ^{- 3 x} + c _{1}}{3 e} )}{2} + \frac{1}{2}

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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((-4e^{-3x}+c_{1})/(3e)))/2+1/2