The general solution of the differential equation $fraction numerator straight y space dx space minus space straight x space dy over denominator straight y end fraction space equals space 0$ is

xy = C

x = Cy²
y = Cx
y = Cx²

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Solution

y = Cx The given differential equation is

fraction numerator straight y space dx minus space straight x space dy over denominator straight y end fraction space equals space 0

fraction numerator straight y space dx space minus space straight x space dy over denominator straight x squared end fraction space equals space 0 space space space space space or space space straight d open parentheses straight x over straight y close parentheses space equals space 0

therefore space space space space space space space space space space straight x over straight y space equals space constant. therefore space space space space space space space space space straight y over straight x space equals space straight C space space or space space space space straight y space equals space Cx therefore space space space space left parenthesis straight C right parenthesis space is space correct space answer.

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