What is the solution for ydx+(e^{-y}+x)dy=0 ?

The solution for ydx+(e^{-y}+x)dy=0 is y=\W(1/(e^{(c_{1))/x}x})+(c_{1})/x

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ydx+(e^{-y}+x)dy=0

y d x + (e^{- y} + x) d y = 0

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

Solution steps

y d x + (e^{- y} + x) d y = 0

Solve exact ODE:

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

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

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What is the solution for ydx+(e^{-y}+x)dy=0 ?
The solution for ydx+(e^{-y}+x)dy=0 is y=\W(1/(e^{(c_{1))/x}x})+(c_{1})/x