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

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

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - 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} + e^{- 2 x - 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^{^{'}} + 5 x^{4} y = x^{4}

\int \frac{y}{x ^{2} + y ^{2}} d y

\frac{\partial}{\partial x} (x y^{2} - y x^{3})

\frac{d}{d x} (1 + 40 x^{3} - 3 x^{5})

x \to 2 lim (1680 x^{3} - 120 x)

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