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

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

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

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

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

Solution steps

\frac{d y}{d x} = \frac{( e ^{- y} + e ^{- 5 x - y} )}{e ^{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 \to 1 lim (- 9 + 3 x^{2})

\int t^{2} - t^{4} \frac{d}{1} d t

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

arctan (\frac{y}{x})

(sin (t))^{^{'}}

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