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})

f (x) = cos (π x)

\frac{\partial}{\partial x} ((7 x + y) (e^{x}))

\frac{d}{d x} (2 cos (x) - 3 sin (x))

\int 9 e^{- x} d x

\frac{d}{d x} ((ln (x - 5) - 2)^{2})

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})