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

e^{x} \cdot 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} \cdot 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

n = 9 \sum \infty (\frac{8}{9})^{- n}

\int \frac{4}{x ^{3} - 4 x ^{2} + 8 x} d x

f (x) = 1 + 2 sin (x), at x = 0

y = x^{2} - 7 x + 7, (6, 1)

x \to π lim (e^{x})

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