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}#