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

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

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(x+ye^{y/x})dx=xe^{y/x}dy

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

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

Solution steps

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

Solve using substitution:

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

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

\frac{d}{d x} (e^{3 l n (x^{2})})

x \to 4 lim (- 2 x)

\frac{2}{( s ^{2} + 4 s + 5 ) s}

\int (\frac{1}{( x - 7 ) ^{2}}) d x

x \to 0 lim (sin (- x^{2}))

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