What is the solution for (1-y/(x^2)e^{y/x})dx+(1+1/x e^{y/x})dy=0 ?

The solution for (1-y/(x^2)e^{y/x})dx+(1+1/x e^{y/x})dy=0 is y=-\W(1/(e^{(x-c_{1))/x}x})x+c_{1}-x

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(1-y/(x^2)e^{y/x})dx+(1+1/x e^{y/x})dy=0

(1 - \frac{y}{x ^{2}} e^{\frac{y}{x}}) d x + (1 + \frac{1}{x} e^{\frac{y}{x}}) d y = 0

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

Solution steps

(1 - \frac{y}{x ^{2}} e^{\frac{y}{x}}) d x + (1 + \frac{1}{x} e^{\frac{y}{x}}) d y = 0

Solve exact ODE:

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

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

What is the solution for (1-y/(x^2)e^{y/x})dx+(1+1/x e^{y/x})dy=0 ?
The solution for (1-y/(x^2)e^{y/x})dx+(1+1/x e^{y/x})dy=0 is y=-\W(1/(e^{(x-c_{1))/x}x})x+c_{1}-x