What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-3x-y} ?

The solution for e^xy(dy)/(dx)=e^{-y}+e^{-3x-y} is y=\W((-4/(e^x)-1/(e^{4x)}+c_{1})/(4e))+1

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e^xy(dy)/(dx)=e^{-y}+e^{-3x-y}

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

y = W (\frac{- \frac{4}{e ^{x}} - \frac{1}{e ^{4 x}} + c _{1}}{4 e}) + 1

Solution steps

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

Solve separable ODE:

y = W (\frac{- \frac{4}{e ^{x}} - \frac{1}{e ^{4 x}} + c _{1}}{4 e}) + 1

y = W (\frac{- \frac{4}{e ^{x}} - \frac{1}{e ^{4 x}} + c _{1}}{4 e}) + 1

y^{3} - (18 x + 2) + 3 x y^{2} y^{^{'}} = 0

y \to - 2 lim (\frac{y ^{3} + 2}{y + 2})

\frac{1}{y ^{2}}

\frac{a}{x}

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

What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-3x-y} ?
The solution for e^xy(dy)/(dx)=e^{-y}+e^{-3x-y} is y=\W((-4/(e^x)-1/(e^{4x)}+c_{1})/(4e))+1