What is the solution for xy^'+y(1+ln(xy))=0 ?

The solution for xy^'+y(1+ln(xy))=0 is y=(e^{(c_{1})/x})/(x)

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xy^'+y(1+ln(xy))=0

x y^{^{'}} + y (1 + ln (x y)) = 0

y = \frac{e ^{\frac{c _{1}}{x}}}{x}

Solution steps

x y^{'} (x) + y (1 + ln (x y)) = 0

Solve using substitution:

y = \frac{e ^{\frac{c _{1}}{x}}}{x}

y = \frac{e ^{\frac{c _{1}}{x}}}{x}

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What is the solution for xy^'+y(1+ln(xy))=0 ?
The solution for xy^'+y(1+ln(xy))=0 is y=(e^{(c_{1})/x})/(x)