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

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

d er i v a t i v e g (x) = 5 tan (3 x)

\int x sin^{2} (8 x) d x

\int 3 e^{x} sin (x) d x

x \to 0 lim (\frac{3 ^{s i n (x)} - 1}{4 x})

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