What is the solution for ye^x(dy)/(dx)=e^{-y}+e^{-3x-y} ?

The solution for ye^x(dy)/(dx)=e^{-y}+e^{-3x-y} is y=\W((-4/(e^x)-1/(e^{4x)}+c_{1})/(4e))+1

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ye^x(dy)/(dx)=e^{-y}+e^{-3x-y}

y e^{x} \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

y = W (\frac{- \frac{4}{e ^{x}} - \frac{1}{e ^{4 x}} + c _{1}}{4 e}) + 1

Solution steps

y e^{x} \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

Solve separable ODE:

y = W (\frac{- \frac{4}{e ^{x}} - \frac{1}{e ^{4 x}} + c _{1}}{4 e}) + 1

y = W (\frac{- \frac{4}{e ^{x}} - \frac{1}{e ^{4 x}} + c _{1}}{4 e}) + 1

y = \frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}} \frac{d y}{d x}

y^{^{'}} = y^{3} e^{- x}

\frac{d V}{d t} = 20 - \frac{5}{100} V, V (0) = 0

y^{^{'}} = x \cdot y - x - 2 \cdot y + 2

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0, y (1) = 1

What is the solution for ye^x(dy)/(dx)=e^{-y}+e^{-3x-y} ?
The solution for ye^x(dy)/(dx)=e^{-y}+e^{-3x-y} is y=\W((-4/(e^x)-1/(e^{4x)}+c_{1})/(4e))+1