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

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

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(e^x+y)dx+(e^y+x)dy=0

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

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

Solution steps

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

Solve exact ODE:

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

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

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