What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-8x-y} ?

The solution for e^xy(dy)/(dx)=e^{-y}+e^{-8x-y} is y=\W((-9/(e^x)-1/(e^{9x)}+c_{1})/(9e))+1

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e^xy(dy)/(dx)=e^{-y}+e^{-8x-y}

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 8 x - y}

y = W (\frac{- \frac{9}{e ^{x}} - \frac{1}{e ^{9 x}} + c _{1}}{9 e}) + 1

Solution steps

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 8 x - y}

Solve separable ODE:

y = W (\frac{- \frac{9}{e ^{x}} - \frac{1}{e ^{9 x}} + c _{1}}{9 e}) + 1

y = W (\frac{- \frac{9}{e ^{x}} - \frac{1}{e ^{9 x}} + c _{1}}{9 e}) + 1

\frac{\partial}{\partial x} ((5 y^{4}) cos (5 x))

f (x) = x + 5, (11, 4)

h (t) = (t + 2)^{\frac{2}{3}} (2 t^{2} - 3)^{3}

\frac{d}{d x} (\frac{e ^{3 x} + e ^{- 3 x}}{x})

\frac{d y}{d t} = (- csc (t) cot (t)) e^{- c s c (t)}

What is the solution for e^xy(dy)/(dx)=e^{-y}+e^{-8x-y} ?
The solution for e^xy(dy)/(dx)=e^{-y}+e^{-8x-y} is y=\W((-9/(e^x)-1/(e^{9x)}+c_{1})/(9e))+1