What is the solution for derivative of xe^y= derivative of x-y ?

The solution for derivative of xe^y= derivative of x-y is y=-\W(x/(e^{-c_{1)-x}})+c_{1}+x

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derivative of xe^y= derivative of x-y

\frac{d}{d x} (x e^{y}) = \frac{d}{d x} (x - y)

y = - W (\frac{x}{e ^{- c_{1} - x}}) + c_{1} + x

Solution steps

\frac{d}{d x} (x e^{y}) = \frac{d}{d x} (x - y)

Solve exact ODE:

y = - W (\frac{x}{e ^{- c_{1} - x}}) + c_{1} + x

y = - W (\frac{x}{e ^{- c_{1} - x}}) + c_{1} + x

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What is the solution for derivative of xe^y= derivative of x-y ?
The solution for derivative of xe^y= derivative of x-y is y=-\W(x/(e^{-c_{1)-x}})+c_{1}+x