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(-1/(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{1}{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{1}{e ^{\frac{c _{1} - e ^{x}}{x}} x}) - \frac{c _{1} - e ^{x}}{x}

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

(x + 1) \frac{d y}{d x} = x + 6

\int - \frac{2}{100 - 9 t ^{2}} d t

x \to - 1 lim (sin (\frac{π x}{6}))

\int 4 x^{\frac{3}{2}} d x

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

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(-1/(e^{(c_{1)-e^x)/x}x})-(c_{1}-e^x)/x