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

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

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

y e^{x} \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

y e^{x} \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

x \frac{d y}{d x} = y^{2} - 9

x^{3} y^{^{'}} = 1 + y

(x^{2} + 9) \frac{d y}{d x} = x y

y^{^{'}} + 16 y = 80, y (0) = - 2

y^{^{'}} = x y^{2} sin (x^{2}), y (0) = 1

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