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

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

e^{x} y \cdot \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} y \cdot \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

\int \frac{1}{( 1 + x ) ^{\frac{3}{2}}} d x

\frac{d ^{3} y}{d x ^{3}} = 4 x^{3} + x

\frac{d ^{2}}{d x ^{2}} (\frac{6}{7 x ^{4}})

\int 2 π x^{3} 1 + 9 x^{4} d x

\frac{\partial}{\partial l} (9 l^{\frac{2}{3}} k^{\frac{1}{3}})

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