What is a solution to the differential equation $xdy/dx=1/y$ ?

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Answer 1 · 2016-07-07T09:32:35

$y = pm sqrt{ ln x^2 + C}$

this is separable

$x dy/dx=1/y$

$y dy/dx=1/x$

$int y dy=int 1/x dx$

$y^2 /2 = ln x + C$

$y^2 = 2 ln x + C = ln x^2 + C$

$y = pm sqrt{ ln x^2 + C}$

What is a solution to the differential equation xdy/dx=1/yxdy/dx=1/y?