What is the solution for e^xy(dy)/(dx)=e^{-y}(1+e^{-2x}) ?

The solution for e^xy(dy)/(dx)=e^{-y}(1+e^{-2x}) is y=\W((-3/(e^x)-1/(e^{3x)}+c_{1})/(3e))+1

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e^xy(dy)/(dx)=e^{-y}(1+e^{-2x})

e^{x} y \frac{d y}{d x} = e^{- y} (1 + e^{- 2 x})

y = W (\frac{- \frac{3}{e ^{x}} - \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

Solution steps

e^{x} y \frac{d y}{d x} = e^{- y} (1 + e^{- 2 x})

Solve separable ODE:

y = W (\frac{- \frac{3}{e ^{x}} - \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

y = W (\frac{- \frac{3}{e ^{x}} - \frac{1}{e ^{3 x}} + c _{1}}{3 e}) + 1

x d y + y d x = 2 d x

\frac{d y}{d x} = - (x y)^{2}

4 t x \frac{d x}{d t} = x^{2} + 1

y^{^{'}} - x^{2} y = 0

\frac{d y}{d x} = y^{3} x

What is the solution for e^xy(dy)/(dx)=e^{-y}(1+e^{-2x}) ?
The solution for e^xy(dy)/(dx)=e^{-y}(1+e^{-2x}) is y=\W((-3/(e^x)-1/(e^{3x)}+c_{1})/(3e))+1