What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-5x-y} ?

The solution for e^xy(dy)/(dx)=e^{-y}+e^{-5x-y} is y=\W((-6/(e^x)-1/(e^{6x)}+c_{1})/(6e))+1

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e^xy(dy)/(dx)=e^{-y}+e^{-5x-y}

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 5 x - y}

y = W (\frac{- \frac{6}{e ^{x}} - \frac{1}{e ^{6 x}} + c _{1}}{6 e}) + 1

Solution steps

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 5 x - y}

Solve separable ODE:

y = W (\frac{- \frac{6}{e ^{x}} - \frac{1}{e ^{6 x}} + c _{1}}{6 e}) + 1

y = W (\frac{- \frac{6}{e ^{x}} - \frac{1}{e ^{6 x}} + c _{1}}{6 e}) + 1

(x^{2} + 8)

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

\int (x^{2} - 3) sin (2 x) d x

\frac{d}{d x} (sin (x) + sin (y) + sin (x + y))

\frac{1}{( x - 2 )}

What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-5x-y} ?
The solution for e^xy(dy)/(dx)=e^{-y}+e^{-5x-y} is y=\W((-6/(e^x)-1/(e^{6x)}+c_{1})/(6e))+1