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

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

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

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

y = ln (- e^{- x} - \frac{1}{3} e^{- 3 x} + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (- e^{- x} - \frac{1}{3} e^{- 3 x} + c_{1})

y = ln (- e^{- x} - \frac{1}{3} e^{- 3 x} + c_{1})

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