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

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

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(x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=0

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

y = ln (ln (x) + c_{1}) x

Solution steps

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

Solve using substitution:

y = ln (ln (x) + c_{1}) x

y = ln (ln (x) + c_{1}) x

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