What is the solution for (e^y-ye^x)dx+(xe^y-e^x)dy=0 ?

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

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(e^y-ye^x)dx+(xe^y-e^x)dy=0

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

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

Solution steps

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

Solve exact ODE:

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

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

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