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

The solution for e^x(ydy)/(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(ydy)/(dx)=e^{-y}+e^{-2x-y}

e^{x} \frac{y 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} \frac{y 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

f (x) = - \frac{1}{( x - 1 ) ^{2}}

(1 - x^{2}) y^{^{''}} + 2 x y^{^{'}} = 0

\int \frac{x}{7 x - 6} d x

\frac{d}{d x} (1 - x^{4})

6 y^{^{''}} + y^{^{'}} - 2 y = 0

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