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

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

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

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

y = - \frac{x}{W ( - \frac{x ^{2}}{c _{1}} )}

Solution steps

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

Solve exact ODE:

y = - \frac{x}{W ( - \frac{x ^{2}}{c _{1}} )}

y = - \frac{x}{W ( - \frac{x ^{2}}{c _{1}} )}

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