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

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

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

(e^{x} y) d y = (e^{- y} + e^{- 2 x - y}) d x

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

Solution steps

(e^{x} y) d y = (e^{- y} + e^{- 2 x - y}) d x

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

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