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

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

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

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

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} + \frac{e ^{- 2 x}}{e ^{y}}

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

y^{^{'}} sin (x) = y ln (y), y (\frac{π}{2}) = e

\frac{d y}{d x} + x^{2} y = 3 x^{2}

y^{^{'}} = e^{y} sin (t)

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

\frac{d y}{d x} y = \frac{sin ( x )}{x ^{3}}

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