What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-4x-y} ?

The solution for e^xy(dy)/(dx)=e^{-y}+e^{-4x-y} is y=\W((-5/(e^x)-1/(e^{5x)}+c_{1})/(5e))+1

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e^xy(dy)/(dx)=e^{-y}+e^{-4x-y}

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 4 x - y}

y = W (\frac{- \frac{5}{e ^{x}} - \frac{1}{e ^{5 x}} + c _{1}}{5 e}) + 1

Solution steps

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 4 x - y}

Solve separable ODE:

y = W (\frac{- \frac{5}{e ^{x}} - \frac{1}{e ^{5 x}} + c _{1}}{5 e}) + 1

y = W (\frac{- \frac{5}{e ^{x}} - \frac{1}{e ^{5 x}} + c _{1}}{5 e}) + 1

\int_{0}^{1} (x^{2} - 3 x + 5) d x

f (x) = \frac{2}{3 x ^{\frac{2}{3}}}, at x = 64

\frac{\partial}{\partial x} (64 - 8 x^{2} - y^{2})

x \to 1 + lim (\frac{1 - x}{x ( x - 1 )})

\frac{d}{d x} (cos^{2} (3 π x))

What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-4x-y} ?
The solution for e^xy(dy)/(dx)=e^{-y}+e^{-4x-y} is y=\W((-5/(e^x)-1/(e^{5x)}+c_{1})/(5e))+1