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

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

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

e^{x} \frac{y 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} \frac{y 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{d y}{d x} - 3 y = ln (3)

t^{4} \cdot y^{^{'}} = 7 y + 4

\frac{d y}{d x} y = x^{2} + 4

\frac{d y}{d x} = \frac{5 e ^{x^{2}} x + 1}{y}

y - 2 y^{^{'}} + 6 y = 0

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