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

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

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

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

y = W (\frac{2 x - e ^{- 2 x} + c _{1}}{2 e ^{3}}) + 1

Solution steps

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

Solve separable ODE:

y = W (\frac{2 x - e ^{- 2 x} + c _{1}}{2 e ^{3}}) + 1

y = W (\frac{2 x - e ^{- 2 x} + c _{1}}{2 e ^{3}}) + 1

(- 4, 7), (- 6, - 4)

\frac{d}{d x} (ln (cos (sin (e^{x^{3}}))))

y^{^{''''}} + 13 y^{^{''}} + 36 y = 0

y = 2 x + 24, y = x^{2}

y^{^{''}} + \frac{3}{x} y^{^{'}} - \frac{15}{x ^{2}} y = 0

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